Question

Chambers is kayaking on a river. She travels 8 miles upstream and 8 miles downstream in a total of 16 hours. In still water, Chambers's speed is 3 miles per hour, to the nearest tenth of a mile per hour, what was the speed of the current of the river?

Answer 1

2.4 miles per hour

Explanation:

Let’s assume that the speed of the current of the river is c miles per hour. When Chambers is kayaking upstream, the speed of the current works against her, so her effective speed is 3 - c miles per hour. When she is kayaking downstream, the speed of the current helps her, so her effective speed is 3 + c miles per hour.

The time it takes Chambers to travel 8 miles upstream is 8 / (3 - c) hours. The time it takes her to travel 8 miles downstream is 8 / (3 + c) hours. The total time for both trips is 16 hours, so we can write an equation to represent this:

8 / (3 - c) + 8 / (3 + c) = 16

Multiplying both sides by (3 - c)(3 + c), we get:

8(3 + c) + 8(3 - c) = 16(3 - c)(3 + c) 24 + 8c + 24 - 8c = 16(9 - c^2) 48 = 144 - 16c^2 16c^2 = 96 c^2 = 6 c = sqrt(6)

So the speed of the current of the river was sqrt(6) miles per hour, which to the nearest tenth of a mile per hour is approximately 2.4 miles per hour.