<p>Maxine skated from her home to the nearby reservoir which is \(13\text{ km}\) away at an average speed of \(x\text{ km/h}\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down an expression in \(x\), for the time taken for Maxine to skate from her home to the reservoir.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">On her return journey, Maxine took another route that is \(3\text{ km}\) shorter and skated at a speed of \((x + 4)\text{ km/h}\).<br>The difference in time taken by Maxine for both journeys is \(120\text{ minutes}\).<br><br>Form an equation in \(x\) and show that it reduces to \(2x^2 + 5x - 52 = 0\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Solve the equation \(2x^2 + 5x - 52 = 0\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the total time taken for both journeys.<span class="inline-marks">[1]</span></div></li></ol>

Maxine skated from her home to the nearby reservoir which is \(13\text{ km}\) away at an average speed of \(x\text{ km/h}\).

Write down an expression in \(x\), for the time taken for Maxine to skate from her home to the reservoir.

On her return journey, Maxine took another route that is \(3\text{ km}\) shorter and skated at a speed of \((x + 4)\text{ km/h}\).
The difference in time taken by Maxine for both journeys is \(120\text{ minutes}\).

Form an equation in \(x\) and show that it reduces to \(2x^2 + 5x - 52 = 0\).

Solve the equation \(2x^2 + 5x - 52 = 0\).

Find the total time taken for both journeys.

Quadratic Expressions, Equations, and Functions

Quadratic Expressions, Equations, and Functions