2005 AMC 10A Problem 7

Problem 7 of 25EasierAlgebra

Josh and Mike live

13

miles apart. Yesterday Josh started to ride his bicycle toward Mike’s house. A little later Mike started to ride his bicycle toward Josh’s house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike’s rate. How many miles had Mike ridden when they met?

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Solution

Let Mike ride

m

miles. Josh rides

\frac{4}{5}

the rate for

2

times the time, so Josh’s distance is

\frac{8}{5}m.

Together they cover

13,

m + \frac{8}{5}m = \frac{13}{5}m = 13,

giving

m = 5.

Thus, the correct answer is B.

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