Mathematics 4024 · O Level · Rates

Rates — practice question

Lara and Marco both cycle $50\text{ km}$ along a cycle trail.
(a)[1]

Lara rides at an average speed of $x\text{ km\/h}$. Write down an expression for the number of hours Lara needs to finish the trail.

(b)[4]

Marco cycles at an average speed of $(x-3)\text{ km\/h}$ and takes $15$ minutes longer than Lara. Hence write an equation and show that it simplifies to $x^2 - 3x - 600 = 0$.

(c)[3]

Find the solutions of the equation $x^2 - 3x - 600 = 0$. Show all your working and give your answers correct to $2$ decimal places.

(d)[2]

Determine the time Marco needs to finish the trail. Give your answer in hours and minutes, correct to the nearest minute.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $50x^{-1}$ or $\frac{50}{x}$

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