1985 AJHSME Problem 13

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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

Distance is equal to rate multiplied by time: \[d = \frac{45}{60} \cdot 4 + \frac{30}{60} \cdot 10 = \boxed{8}.\] The answer is $\text{(B)}.$

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