Two cars travel the same distance. The ratio of their distances is $3 : 2$ and the ratio of their speeds is $5 : 4$ . What is the ratio of the times taken by the two cars to travel that distance?

hard 4 marks Class 8 · Mathematics · Direct and Inverse Proportions

Answer

6:5

The correct answer is 6:5 — Multiply: $\frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5}$ .

Step-by-step solution

Recall that time $t = \frac{distance}{speed}$ .
Express the time ratio: $\frac{t _{1}}{t _{2}} = \frac{d _{1} / s _{1}}{d _{2} / s _{2}} = \frac{d _{1}}{d _{2}} \times \frac{s _{2}}{s _{1}}$ .
Substitute the given ratios: $\frac{d _{1}}{d _{2}} = \frac{3}{2}$ and $\frac{s _{2}}{s _{1}} = \frac{4}{5}$ .
Multiply: $\frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5}$ .

Common mistake: Multiplying the ratios of distances and speeds directly instead of using the reciprocal for speed.

Concept tested: Inverse Proportion (time vs. speed)