Chapter A.8, Problem 27AYU

To determine

To find: A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was $1.5$ hours. What is the speed of the current.

Answer to Problem 27AYU

The speed of the current is 5.

Explanation of Solution

Upstream $=\frac{10}{15-x}$ and down stream $=\frac{10}{15+x}$

Therefore,

$\frac{10}{15-x}+\frac{10}{15+x}=1.5$

$\frac{10\left(15+x\right)+10\left(15-x\right)}{\left(15-x\right)\left(15+x\right)}=25-x^2=0$

That is $x=\pm 5$.