<p>Victor cycles at a speed of \(x\) km/h up a \(30\) km slope.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down, in terms of \(x\), the number of hours he took to cycle up the slope.<span class="inline-marks">[1]</span></div></li></ol>
<p>He then cycles at a speed of \((x + 5)\) km/h down the same slope.</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Write down, in terms of \(x\), the number of hours he took to cycle down the slope.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">The difference in time taken is \(18\) minutes.<br>Write down an equation in \(x\) to represent this information and show that it reduces to</div><div class="list-item-paragraph" style="text-align: center">\(x^2 + 5x - 500 = 0.\)<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Solve the equation \(x^2 + 5x - 500 = 0\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Hence, calculate the total time taken, in hours and minutes, Victor took for the whole journey.</div></li></ol>

Victor cycles at a speed of \(x\) km/h up a \(30\) km slope.

Write down, in terms of \(x\), the number of hours he took to cycle up the slope.

He then cycles at a speed of \((x + 5)\) km/h down the same slope.

Write down, in terms of \(x\), the number of hours he took to cycle down the slope.

The difference in time taken is \(18\) minutes.
Write down an equation in \(x\) to represent this information and show that it reduces to

Solve the equation \(x^2 + 5x - 500 = 0\).

Hence, calculate the total time taken, in hours and minutes, Victor took for the whole journey.

RSS 2EM EOY P2 2023 Q12

RSS 2EM EOY P2 2023 Q12