# 1984 AHSME Problems/Problem 7

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## Problem

When Dave walks to school, he averages $90$ steps per minute, and each of his steps is $75$ cm long. It takes him $16$ minutes to get to school. His brother, Jack, going to the same school by the same route, averages $100$ steps per minute, but his steps are only $60$ cm long. How long does it take Jack to get to school?

$\mathrm{(A) \ }14 \frac{2}{9} \text{minutes} \qquad \mathrm{(B) \ }15 \text{minutes}\qquad \mathrm{(C) \ } 18 \text{minutes}\qquad \mathrm{(D) \ }20 \text{minutes} \qquad \mathrm{(E) \ } 22 \frac{2}{9} \text{minutes}$

## Solution

At $90$ steps per minute and $75 cm$ per step, Dave walks at a rate of $90\times75$ cm per minute, and with $16$ minutes, the distance Dave walks to school is $90\times75\times16$. Also, at $100$ steps per minute and $60$ cm per step, Jack walks at a rate of $100\times60$ cm per minute. Jack must walk $90\times75\times16$ cm, so it takes him $\frac{90\times75\times16}{100\times60}$ minutes. Canceling some of the factors, this comes out to $18 \text{minutes}, \boxed{\text{C}}$.

## See Also

 1984 AHSME (Problems • Answer Key • Resources) Preceded byProblem 6 Followed byProblem 8 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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