Question

Along the route of a bicycle race, $7$ water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also $2$ repair stations evenly spaced between the start and finish lines. The $3$ rd water station is located $2$ miles after the $1$ st repair station. How long is the race in miles?

$8$

$16$

$24$

$48$

$96$

Video solution:

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Written solution:

The $3$ rd water station is located $\frac{3}{8}$ of the way along the race (the water stations split the race up into $8$ equal spaces).

The first repair station is located $\frac{1}{3}$ of the way along the race. The distance between the two is $\dfrac{3}{8} - \dfrac{1}{3} = \dfrac{1}{24}$ the length of the race. We know that this equals $2,$ which means the race is $24 \cdot 2 = 48$ miles long.

Thus, D is the correct answer.

2023 AMC 8 Problem 13

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Problem 13 in Other Years