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PSLE

PSLE Foundation Mathematics

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">A train is travelling at a constant speed of $x$ km/h for $40$ km. Then it slows down and travels $\left(25 + \frac{x}{5}\right)$ km at a constant speed of $15$ km/h slower. Given that it takes $12$ minutes shorter to travel the first $40$ km, form an equation and show that it reduces down to $\frac{200 + x}{5x} = \frac{125 + x}{5x - 75}$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Solve the equation in <strong>(i)</strong>. Hence, or otherwise, find the average speed of the train for the whole journey.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-content"><span class="list-item-text">After the train slows down, it takes $72$ seconds to pass a lamp post. Find the length of the train.</span><span class="inline-marks">[2]</span></div></li></ol>

A train is travelling at a constant speed of $x$ km/h for $40$ km. Then it slows down and travels $\left(25 + \frac{x}{5}\right)$ km at a constant speed of $15$ km/h slower. Given that it takes $12$ minutes shorter to travel the first $40$ km, form an equation and show that it reduces down to $\frac{200 + x}{5x} = \frac{125 + x}{5x - 75}$.

After the train slows down, it takes $72$ seconds to pass a lamp post. Find the length of the train.

Applications of Linear Equations in Real Life

Speed, Distance and Time

Average Speed over a Journey

IP1 Class Test (May 2025) Q13

Ratio, Rate and Speed

Linear Equations and Inequalities

<p>A lawn mower has a blade of breadth $0.75$ m, and its two front wheels are identical of diameter $20$ cm, its two rear wheels are identical of diameter $40$ cm. A gardener uses this lawn mower to mow a square lawn of dimension of $18$ m by $18$ m. He alternates his mowing directions, as shown in the figure below, at a speed of $5$ m/min.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767770230557-ep6ty5s4h1v.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzAyMzA1NTctZXA2dHk1czRoMXYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU0ODE1OCwiZXhwIjoxNzkzNTQ4NDU4fQ.WZfP3WUjgDccEW_oVRY-VGMjpTmP1rYWOx1NYAl6XDM" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Assuming there is no overlapping of mowing areas, find</p>
<ol class="abc-list"><li data-list-item-id="item-1767770241397-x243aajbw" data-list-item-path="item-1767770241397-x243aajbw"><div class="list-item-paragraph">the number of times he needs to move from one side to the opposite side of the lawn to finish mowing the whole area of the lawn,</div></li><li data-list-item-id="item-1767770241933-2iwwf0hbj" data-list-item-path="item-1767770241933-2iwwf0hbj"><div class="list-item-paragraph">the number of rotations of the front and rear wheels, respectively, to finish mowing from one side to the opposite side, ignoring the length of the mower (giving your answers to the nearest integer),</div></li><li data-list-item-id="item-1767770242517-byd10cg6g" data-list-item-path="item-1767770242517-byd10cg6g"><div class="list-item-paragraph"><br>the least possible time needed for the gardener to fully mow the lawn.</div></li></ol>
<p>Clarification for (c): the intended model counts time along the straight mowing strips only, excluding the turns and movement between strips. The source gives no turning model, so it does not determine the actual minimum total journey time.</p>

A lawn mower has a blade of breadth $0.75$ m, and its two front wheels are identical of diameter $20$ cm, its two rear wheels are identical of diameter $40$ cm. A gardener uses this lawn mower to mow a square lawn of dimension of $18$ m by $18$ m. He alternates his mowing directions, as shown in the figure below, at a speed of $5$ m/min.

Assuming there is no overlapping of mowing areas, find

Clarification for (c): the intended model counts time along the straight mowing strips only, excluding the turns and movement between strips. The source gives no turning model, so it does not determine the actual minimum total journey time.

Perimeter and Area of Rectangles and Squares

Circumference and Area of Circles

Perimeter and Area of Common Plane Figures

Perimeter and Area of Plane Figures

Arc Length and Area of Sector

<p>A roller brush used for wall-painting has a circular cross section of diameter $8$ cm, and the breadth of the roller is $21$ cm. A painter uses this roller brush to paint a wall of breadth $4.2$ m and height $5$ m. He paints in vertical rectangular paint columns of breadth $21$ cm and in a speed of $10$ cm/s in the vertical direction. </p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767690677788-jn9mox3202r.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTA2Nzc3ODgtam45bW94MzIwMnIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU0ODE1OCwiZXhwIjoxNzkzNTQ4NDU4fQ.xU1ByVueKWzYGR2yLtFcLeTkcz05XVLTKDUTMDHegxU" style="max-width: min(340px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Assuming there are no overlapping paint columns, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the number of paint columns needed to finish painting the whole area of the wall,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of rotations of the roller to finish painting one column, correcting your answer to the nearest integer,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the least possible time needed for the painter to fully paint the wall.</span></div></li></ol>

A roller brush used for wall-painting has a circular cross section of diameter $8$ cm, and the breadth of the roller is $21$ cm. A painter uses this roller brush to paint a wall of breadth $4.2$ m and height $5$ m. He paints in vertical rectangular paint columns of breadth $21$ cm and in a speed of $10$ cm/s in the vertical direction. 

Assuming there are no overlapping paint columns, find

the number of paint columns needed to finish painting the whole area of the wall,

the number of rotations of the roller to finish painting one column, correcting your answer to the nearest integer,

the least possible time needed for the painter to fully paint the wall.

<p>In this question, the average tangential speed along the circular path is being calculated by the following formula:\[\text{Average tangential speed} = \frac{\text{Total circular distance travelled}}{\text{Total time taken}}\]The Singapore Flyer is one of the world’s most famous Ferris wheels, which has a radius of $75$ m.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Given that it takes $30$ minutes for the Singapore Flyer to finish one full rotation, find the average tangential speed of the Singapore Flyer in one full rotation in m/s.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Find the average speed of ascending in vertical direction, for a capsule of the Singapore Flyer to travel from the lowest point to the highest point.</div></li></ol>
<p>The London Eye is another famous Ferris wheel in the world, which also finishes one full rotation in $30$ minutes.</p>
<ol class="i-list" start="3"><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">Given that the ratio of the radius of the Singapore Flyer to the radius of the London Eye is $5 : 4$, find the average tangential speed of the London Eye in one full rotation in m/s.</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">Using your answer in (iii), find the average speed of descending in vertical direction, for a capsule of the London Eye to travel from the highest point to the lowest point.</div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767674389740-uhh3znrfqv.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2NzQzODk3NDAtdWhoM3pucmZxdi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTQ4MTU4LCJleHAiOjE3OTM1NDg0NTh9.xycrQpjhPfT0CIeff5BwSBDzNd-Vy-6ylLyL42PPkPM" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Use the stated dimensions as a mathematical model and assume both wheels rotate uniformly. Then a half-turn takes half the full-turn time.</p>

In this question, the average tangential speed along the circular path is being calculated by the following formula:\[\text{Average tangential speed} = \frac{\text{Total circular distance travelled}}{\text{Total time taken}}\]The Singapore Flyer is one of the world’s most famous Ferris wheels, which has a radius of $75$ m.

Given that it takes $30$ minutes for the Singapore Flyer to finish one full rotation, find the average tangential speed of the Singapore Flyer in one full rotation in m/s.

Find the average speed of ascending in vertical direction, for a capsule of the Singapore Flyer to travel from the lowest point to the highest point.

The London Eye is another famous Ferris wheel in the world, which also finishes one full rotation in $30$ minutes.

Given that the ratio of the radius of the Singapore Flyer to the radius of the London Eye is $5 : 4$, find the average tangential speed of the London Eye in one full rotation in m/s.

Using your answer in (iii), find the average speed of descending in vertical direction, for a capsule of the London Eye to travel from the highest point to the lowest point.

Use the stated dimensions as a mathematical model and assume both wheels rotate uniformly. Then a half-turn takes half the full-turn time.

Dividing Quantities in a Given Ratio

Speed

<p>A freight train is travelling at a constant speed of $72$ km/h.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">A passenger train is travelling towards the freight train at a constant speed of $108$ km/h. A passenger on the passenger train observes that it takes $21$ seconds from the moment the two trains meet each other until the two trains completely separate. Given that the passenger train is $450$ m in length, find the length of the freight train.</span></div></li><li><div class="list-item-paragraph">The freight train is entering a tunnel. Given that it takes $1\frac{2}{3}$ minutes for the freight train to completely leave the tunnel, using your answer in <strong>(i)</strong>, find the length of the tunnel.</div></li></ol>

A freight train is travelling at a constant speed of $72$ km/h.

A passenger train is travelling towards the freight train at a constant speed of $108$ km/h. A passenger on the passenger train observes that it takes $21$ seconds from the moment the two trains meet each other until the two trains completely separate. Given that the passenger train is $450$ m in length, find the length of the freight train.

Relative Speed

<p>The speed of sound in air is approximately $343$ m/s. Using this speed of sound, consider the following circumstances:</p>
<ol class="i-list"><li><div class="list-item-paragraph">At an observation point, a lightning flash is seen $5.3$ seconds before a thunder is heard. Find the distance between the observation point and where the lightning happens. You may assume that time lapse between the occurrence of the lightning flash and its detection at the observation point is negligible.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-22-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1pLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU0ODE1OCwiZXhwIjoxNzkzNTQ4NDU4fQ.QvuNnwfC-zpbEqwQNt5udCJ0fvUGv3Et8zHQOcgGR4M" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">A ship whistles at some point on the sea, and two beacons, Beacon A and Beacon B, hear the whistle. Given that Beacon A hears the whistle $2.1$ seconds after Beacon B does, and that the distance between the ship and Beacon B is $686$ m when the ship whistles. Find the distance between the ship and Beacon A when the ship whistles.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-22-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1paS1kaWFncmFtLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTM1NDgxNTgsImV4cCI6MTc5MzU0ODQ1OH0.imAs76Sx5yNxRQc5ybk01fPoEPGmMBNaeWKYUBabuOQ" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">An engine is started at some point in the middle of two mountains. After $2.5$ seconds and $4$ seconds respectively, two echoes are heard. Assuming the engine and the two mountains lie on the same straight line, find the horizontal distance between the two mountains.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-22-iii-diagram-624x124.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1paWktZGlhZ3JhbS02MjR4MTI0LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTM1NDgxNTgsImV4cCI6MTc5MzU0ODQ1OH0.bTYukxvjTXm4diWFKC8rkzPUqH3nAF9BeKmSynTQxc0" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

The speed of sound in air is approximately $343$ m/s. Using this speed of sound, consider the following circumstances:

At an observation point, a lightning flash is seen $5.3$ seconds before a thunder is heard. Find the distance between the observation point and where the lightning happens. You may assume that time lapse between the occurrence of the lightning flash and its detection at the observation point is negligible.

An engine is started at some point in the middle of two mountains. After $2.5$ seconds and $4$ seconds respectively, two echoes are heard. Assuming the engine and the two mountains lie on the same straight line, find the horizontal distance between the two mountains.

<p>In the diagram, $P$, $Q$ and $R$ represent three reservoirs.</p>
<p>$P$ is $22$ km from $Q$ on a bearing of $140{}^\circ$ and $R$ is $20$ km from $P$ on a bearing of $290{}^\circ$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767444241225-yqhegew0xe.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDQyNDEyMjUteXFoZWdldzB4ZS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTQ4MTU4LCJleHAiOjE3OTM1NDg0NTh9.Q09CxnXwd1s4LYa1DLltLeBP57Qwpa-BfnXBnVTyKkg" style="max-width: min(250px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Calculate the bearing of $Q$ from $P$.</span></div></li><li><div class="list-item-paragraph">A cyclist leaves $P$ and cycled along $PQ$ towards $Q$ at a steady speed of $10$ km/h.</div><div class="list-item-paragraph">He stops at a point $S$ which is due east of $R$.</div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Mark the point $S$ on the diagram.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the distance $PS$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the time taken to reach $S$ from $P$, giving your answer in minutes.</span></div></li></ol></li><li><div class="list-item-paragraph">A tower of height $60$ m is located at $P$.</div><div class="list-item-paragraph">What is the angle of elevation of the top of the tower from the cyclist at point $S$?</div></li></ol>

In the diagram, $P$, $Q$ and $R$ represent three reservoirs.

$P$ is $22$ km from $Q$ on a bearing of $140{}^\circ$ and $R$ is $20$ km from $P$ on a bearing of $290{}^\circ$.

Calculate the bearing of $Q$ from $P$.

Sine Rule

Angles of Elevation and Depression

Bearings

Navigational Trigonometry: Analyzing Bearings and Positions of Three Reservoirs

Trigonometry

<p>A boat is at $C$, $150$ m away from the foot of cliff at $B$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767442586890-wcfoy3litca.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDI1ODY4OTAtd2Nmb3kzbGl0Y2EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU0ODE1OCwiZXhwIjoxNzkzNTQ4NDU4fQ.3Dx9TFdP8oHmes_a3ZMBRlXHgVOMlDTt8JvOnR8vzdA" style="max-width: min(230px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">The angle of elevation of the top of the cliff $A$ from the boat is $23{}^\circ$.</div><div class="list-item-paragraph">Find the height of the cliff.</div></li><li><div class="list-item-content"><span class="list-item-text">If the boat moved $50$ m from $C$ towards the cliff at $D$, find the angle of elevation from the boat to the top of the cliff.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the boat moved from $C$ to the foot of the cliff $B$ in $2$ minutes, find the speed of the boat in km/h.</span></div></li></ol>

A boat is at $C$, $150$ m away from the foot of cliff at $B$.

If the boat moved $50$ m from $C$ towards the cliff at $D$, find the angle of elevation from the boat to the top of the cliff.

If the boat moved from $C$ to the foot of the cliff $B$ in $2$ minutes, find the speed of the boat in km/h.

Trigonometry and Boat Speed

<p>The Earth is approximately $150$ gigametres away from the Sun.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Express $150$ gigametres in kilometres, giving your answer in standard form</div></li><li><div class="list-item-paragraph">Light take $3\frac{1}{3}$ nanoseconds to travel $1$ metre. Calculate the time light takes to travel from the Sun to the Earth, giving your answer in seconds, in standard form.</div></li></ol>

The Earth is approximately $150$ gigametres away from the Sun.

Converting Metric Prefixes Using Powers of Ten

Calculations in Standard Form

Standard Form in Astronomy

Standard Form and Compound Interest

<p>The Earth is approximately $0.787$ terametres (Tm) (1 tera $=\mathrm{ }{{10}^{12}}$) away from the Jupiter.<br>Light takes about $8.936$ nanoseconds (1 nano $=\mathrm{ }{{10}^{-9}}$) to travel $3$ metres.<br>Leaving your answers in standard form,</p>
<ol class="i-list"><li><div class="list-item-paragraph">express $0.787$ Tm in m.</div></li><li><div class="list-item-paragraph">calculate the time taken, in seconds, for light to travel from the Earth to Jupiter.</div></li></ol>

The Earth is approximately $0.787$ terametres (Tm) (1 tera $=\mathrm{ }{{10}^{12}}$) away from the Jupiter.
Light takes about $8.936$ nanoseconds (1 nano $=\mathrm{ }{{10}^{-9}}$) to travel $3$ metres.
Leaving your answers in standard form,

Common Prefixes in our Daily Life

<p>Mr Sim is driving at a constant speed of $80$ km/h.  What distance will he travel in $3$ hours $45$ minutes?</p>

Mr Sim is driving at a constant speed of $80$ km/h.  What distance will he travel in $3$ hours $45$ minutes?

Distance Travelled Using Speed × Time

<p>Nicholas took $2$ minutes $16$ seconds to complete an $800$-metre race.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Express $2$ minutes $16$ seconds in minutes.</div></li><li><div class="list-item-paragraph">Calculate his average speed in kilometres per hour.</div></li></ol>

Nicholas took $2$ minutes $16$ seconds to complete an $800$-metre race.

Converting Time and Finding Speed

<p>A train travels $21.4$ km in $18$ minutes. Find the speed in</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">km/h	</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">m/s</div></li></ol></div></div></div>

A train travels $21.4$ km in $18$ minutes. Find the speed in

Converting Units of Rates and Speed

Finding Train Speed in km/h and m/s

<p>Steven drove $170$ kilometres at an average speed of $55$ km/h.  Calculate the time, in hours and minutes, he took for the journey.</p>

Steven drove $170$ kilometres at an average speed of $55$ km/h.  Calculate the time, in hours and minutes, he took for the journey.

Calculating Travel Time from Speed and Distance

<p>A car begins its journey at $2.45$ pm and reaches its destination at $3.50$ pm. The distance travelled by the car is $175$ km. Calculate the speed in</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">km/h</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">m/s</div></li></ol></div></div></div>

A car begins its journey at $2.45$ pm and reaches its destination at $3.50$ pm. The distance travelled by the car is $175$ km. Calculate the speed in

Speed Calculation from Time and Distance

<p>A freight train travels at a constant speed of $72\text{ km/h}$.</p>
<ol class="i-list"><li data-list-item-id="item-1760834328190-n3a8cpwvf" data-list-item-path="item-1760834328190-n3a8cpwvf"><div class="list-item-paragraph">A passenger train is travelling towards the freight train at a constant speed of $108$ km/h. A passenger on the passenger train observes that it takes $21$ seconds from the moment the two trains meet each other until the two trains completely separate. Given that the passenger train is $450$ m in length, find the length of the freight train.</div></li><li data-list-item-id="item-1760834328939-n09xn9suv" data-list-item-path="item-1760834328939-n09xn9suv"><div class="list-item-paragraph">The freight train is entering a tunnel. Given that it takes $1\frac{2}{3}$ minutes for the freight train to completely leave the tunnel, using your answer in <strong>(i)</strong>, find the length of the tunnel.</div></li></ol>

A freight train travels at a constant speed of $72\text{ km/h}$.

IP1U9 HOT Q2

<p>A bus travels at a speed of ${15\ \mathrm{m/s}}$ from Town ${X}$ to Town ${Y}$. Towns ${X}$ and ${Y}$ are ${48\ \mathrm{km}}$ apart.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Change ${15\ \mathrm{m/s}}$ into ${\mathrm{km/h}}$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Calculate the time taken for the bus to travel from Town ${X}$ to Town ${Y}$.</div><div class="list-item-paragraph">Give your answer in minutes and seconds.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">The bus continued to travel ${37\ \mathrm{km}}$ from Town ${Y}$ to Town ${Z}$ in ${39}$ minutes and ${40}$ seconds. Calculate the average speed for the whole journey from Town ${X}$ to Town ${Z}$.Give your answer in kilometres per hour.</div><p style="text-align: right;">[3]</p></li></ol>

A bus travels at a speed of ${15\ \mathrm{m/s}}$ from Town ${X}$ to Town ${Y}$. Towns ${X}$ and ${Y}$ are ${48\ \mathrm{km}}$ apart.

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