The speed of the current in a stream is 2.4 mi/hr. It takes a canoeist 60 minutes longer to paddle 1.7 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.
A)3.7 mi/hr
B)4.9 mi/hr
C)2.4 mi/hr
D)3.1 mi/hr
E)6.3 mi/hr

Question

Quizplus · Accepted Answer

The canoeist's rate in still water can be found by setting up equations based on the distance, rate, and time for both upstream and downstream travel. Let $x$ be the canoeist's rate in still water. The effective rate downstream is $x + 2.4$ mi/hr and upstream is $x - 2.4$ mi/hr. The time to travel 1.7 miles downstream is $\frac{1.7}{x + 2.4}$ hours, and upstream is $\frac{1.7}{x - 2.4}$ hours. The problem states that it takes 60 minutes (or 1 hour) longer to paddle upstream, so we have the equation: $\frac{1.7}{x - 2.4} - \frac{1.7}{x + 2.4} = 1$. Solving this equation for $x$ gives the canoeist's rate in still water, which is approximately 3.7 mi/hr when rounded to the nearest tenth.

The Speed of the Current in a Stream Is 2