Question

Roy kayaked up the river and then back in a total of 6 hours. The trip was 4 miles each way and the current was difficult. If Roy kayaked at a speed of 6 mph, what was the speed of the current? Round your answer to 2 decimal places.

Answer 1

9514 1404 393

Answer:

5.29 mph

Explanation:

The time is given by ...

time = distance/speed

Then the total time for the round trip, using x as the speed of the current, is ...

4/(6+x) +4/(6-x) = 6

where distances are in miles, time is in hours, and speed is in miles per hour.

Multiplying by the product of the denominators, we have ...

4(6 -x) +4(6 +x) = 6(6 -x)(6 +x)

48 = 6(36 -x^2)

x^2 = 28

x = √28 ≈ 5.29 . . . . miles per hour

The speed of the current was about 5.29 miles per hour.

_____

The trip upstream took about 5 hours and 39 minutes; the trip downstream took about 21 minutes.