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Algebra Difficulty 3.7 AMC 10/12 Find the answer Canada

Jiwei and Hari entered a race. Hari finished the race in $\frac{4}{5}$ of the time it took Jiwei to
finish. The next time that they raced the same distance, Jiwei increased
his average speed from the first race by $x$ %, while Hari maintained the same
average speed as in the first race. In this second race, Hari finished
the race in the same amount of time that it took Jiwei to finish. The
value of $x$ is

Pick one

Solution

Suppose that the length of the race was $d \text{ m}$ .

Suppose further that Jiwei finished the first race in $t \text{ s}$ .

Since Hari finished in $\dfrac{4}{5}$
of the time that Jiwei took, then Hari finished in $\dfrac{4}{5}t \text{ s}$ .

Since speed equals distance divided by time, then Jiwei’s average speed
was $\dfrac{d}{t} \text{ m/s}$ and
Hari’s average speed was $\$\dfrac{d}{4t/5} = \dfrac{5}{4} \cdot \dfrac{d}{t} \text{}$ m/s}$.

For Jiwei to finish in the same time as Hari, Jiwei must increase his
average speed from $\$\dfrac{d}{t} \text{}$
m/s} $to$ $\dfrac{5}{4}\cdot \dfrac{d}{t} \text{}$ m/s}$.

This is an increase of one-quarter over the original speed, or an
increase of $25\%$ . Thus, $x = 25$ .

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