motorboat could go

Question

The motorboat could go 15 miles downstream in 3 hours, but took 2 hours longer to go 10 miles upstream.  What is the speed of the current?

Answer 1

Let r = the speed of the motorboat

Let c = the speed of the current

d = rt

15 = (r + c)3

10 = (r - c)5

15 = 3r + 3c       Multiply both sides of this equation by 5.

10 = 5r - 5c        Multiply both sides of this equation by 3.

75 = 15r + 15c

30 = 15r - 15c    Add these two equations together.

105 = 30r

3.5 mph = r

15 = 3(3.5) + 3c

15 = 10.5 + 3c

4.5 = 3c

1.5 mph = c