Mathematics 0580 · IGCSE · Equations

Equations — practice question

Luigi and Alfredo take part in a 10 km race. Luigi’s average speed was $x$ km/h. Alfredo’s average speed was 0.5 km/h less than Luigi’s average speed.
(a)[1]

Write down an expression, in terms of $x$, for the time Alfredo needed to complete the race.

(b(i))[4]

Show that this leads to $2x^2 - x - 40 = 0$.

(b(ii))[4]

Use the quadratic formula to solve $2x^2 - x - 40 = 0$. Show all your working and give your answers correct to 2 decimal places.

(b(iii))[3]

Work out the time Luigi needed to complete the 10 km race. Give your answer in hours and minutes, correct to the nearest minute.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: This gives $\frac{10}{x - 0.5}$.

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