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Problem 574

Algebra Difficulty 2.6 Multiple choice CEMC Cayley · Canada · 2023

Megan and Hana raced their remote control cars for 100 m.

The two cars started at the same time.

The average speed of Megan’s car was $\frac{5}{4}$ m/s.

Hana’s car finished 5 seconds before Megan’s car.

What was the average speed of Hana’s car?

Pick one

Official solution

Megan’s car travels 100 m at $\dfrac{5}{4}$ m/s, and so takes $\dfrac{100\text{ m}}{5/4\text{ m/s}} = \dfrac{400}{5}\text{ s} = 80\text{ s}$ .

Hana’s car completes the 100 m in 5 s fewer, and so takes 75 s.

Thus, the average speed of Hana’s car was $\dfrac{100\text{ m}}{75\text{ s}} = \dfrac{100}{75}\text{ m/s} = \dfrac{4}{3}\text{ m/s}$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.