what is the speed of the current?

Question

A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles. Find the speed of the current.

Answer 1

distance=rate*time

16=r*(20/60)

16=r*(1/3)

48 mph=r (with the current)

16=r*(30/60)

16=r*(1/2)

32 mph=r (against the current)

let c=rate of the current

r+c=48 (with the current)

r-c=32 (against the current)

add the two equations

2r=80

r=40 mph

r+c=48

40+c=48

c=8 mph for the speed of the current, or...

r-c=32

40-c=32

-c=-8

c=8 mph again