Kelsey is kayaking on a river. She travels 5 miles upstream and 5 miles downstream in a total of 6 hours. More in despcription.

Question

Kelsey is kayaking on a river. She travels 5 miles upstream and 5 miles downstream in a total of 6 hours. In still water, Kelsey can travel at an average speed of 3 miles per hour. What is the average speed of the river's current?

Answer 1

Kyle, d = rt, right? This means that t = d/r.

 

If we call the rate of the current c, then her rate upstream is hindered by the current and is 3 - c. Downstream is 3 + c.

 

The total time is 6 hours...

 

5/(3 - c) + 5/(3 + c) = 6

 

Once we put everything over the same denominator, we don't need it anymore.

 

5(3 + c) + 5(3 - c) = 6(3 - c)(3 + c)

 

15 + 5c + 15 - 5c = 54 - 6c²

30 = 54 - 6c²

6c² = 24

c² = 4

c = 2

 

2 mph