Question

A steamer going downstream traveled the distance between two ports in 3 hours. The return trip took 3 hours 40 minutes. Find the speed of the water current if the speed of the steamer in still water is 18 mph.

Answer 1

Answer:

1.8 mph

Step-by-step explanation:

Speed of the steamer in still water is 18 mph.

Speed of the current = x mph.

1. The steamer going downstream traveled the distance between two ports in 3 hours. Traveling downstream the current "helps" the steamer, then the speed is 18 + x mph.

The distance traveled downstream = 3(18 + x) miles.

2. The steamer going upstream traveled the distance between two ports in 3 hours 40 minutes that is $3\frac{2}{3}$ hours. Traveling upstream the current "interferes" the steamer, then the speed is 18 - x mph.

The distance traveled upstream $3\dfrac{2}{3}(18-x)$ miles.

3. The distances are the same, so

$3(18+x)=3\dfrac{2}{3}(18-x)$

Solve this equation:

$3(18+x)=\dfrac{11}{3}(18-x)\\ \\9(18+x)=11(18-x)\\ \\162+9x=198-11x\\ \\9x+11x=198-162\\ \\20x=36\\ \\x=1.8\ mph$