AMC 12 Mock Exam 1 Problem 1

Problem 1 of 25

A courier rides from a depot to a warehouse at a steady $12$ miles per hour. After waiting $20$ minutes at the warehouse while a package is loaded, she rides back to the depot along the same route at a steady $18$ miles per hour. From the moment she leaves the depot until the moment she returns, exactly $5$ hours and $20$ minutes elapse. How many miles is the warehouse from the depot?

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Solution

Let $d$ be the distance in miles. The riding time is $\frac{d}{12}+\frac{d}{18}=\frac{5d}{36}$ hours, and the waiting time is $\frac13$ hour. Since $5\text{ h }20\text{ min}=\frac{16}{3}$ hours, $\frac{5d}{36}+\frac13=\frac{16}{3}\implies \frac{5d}{36}=5\implies d=36.$

Tagged: rates and elapsed time

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