Question

A boat has a speed of $15$ mph in still water. In a stream that has a current of $5$ mph it travels a certain distance downstream and returns. The ratio of the average speed for the round trip to the speed in still water is:

$\dfrac54$

$\dfrac11$

$\dfrac89$

$\dfrac78$

$\dfrac98$

Answer: C

Concepts:distance rate and time relative speed harmonic mean

Difficulty rating: 1580

Small Hint:

The downstream and upstream speeds are $20$ mph and $10$ mph

Big Hint:

For equal distances, divide twice the distance by $\frac{d}{20}+\frac{d}{10}$

Solution:

For a one-way distance $d,$ the total time is $\frac d{20}+\frac d{10}=\frac{3d}{20}.$ Thus the round-trip average speed is $\frac{2d}{\frac{3d}{20}}=\frac{40}{3}.$ Its ratio to $15$ is $\frac{\frac{40}{3}}{15}=\frac89.$

Thus, the correct answer is C.

1954 AMC 12 Problem 36

Answer: C

Difficulty rating: 1580

Small Hint:

Big Hint:

Solution:

Problem 36 in Other Years