1985 AJHSME Problems/Problem 13

Problem

If you walk for $45$ minutes at a rate of $4 \text{ mph}$ and then run for $30$ minutes at a rate of $10\text{ mph}$ , how many miles will you have gone at the end of one hour and $15$ minutes?

$\text{(A)}\ 3.5\text{ miles} \qquad \text{(B)}\ 8\text{ miles} \qquad \text{(C)}\ 9\text{ miles} \qquad \text{(D)}\ 25\frac{1}{3}\text{ miles} \qquad \text{(E)}\ 480\text{ miles}$

Solution

$45$ minutes is $\frac{3}{4}$ of an hour, so the walking contributes $\frac{3\text{ hr}}{4}\times \frac{4 \text{ miles}}{1\text{ hr}}=3\text{ miles}$ .

Similarly, $30$ minutes is $\frac{1}{2}$ of an hour, so the running adds $\frac{1\text{ hr}}{2}\times\frac{10\text{ miles}}{1\text{ hr}}=5\text{ miles}$ .

Their total is $3\text{ miles}+5\text{ miles}=8\text{ miles}$ , which is $\boxed{\text{B}}$

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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1985 AJHSME Problems/Problem 13

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