a motorboat can go 8 miles downstream in 20 minutes It takes

a motorboat can go 8 miles downstream in 20 minutes. It takes the same motorboat 30 minutes to go back upstream the same 8 miles. find the speed of the current.

Solution

Let m = speed of motorboat
and c = speed of current
.
When going downstream, current speed is added to boat speed -- and, the total speed is \"8 miles downstream in 20 minutes\"
.
To convert to \"miles per hour\" we multiply by 60 mins per 1 hour:
(8 miles/20 mins) * (60 mins/1 hour) = 24 mph
.
This gives us our first equation (1):
m+c = 24
.
When going upstream, the boat speed is reduced by the current -- and, the total speed is \"8 miles in 30 minutes\".
To convert to \"miles per hour\" we multiply by 60 mins per 1 hour:
(8 miles/30 mins) * (60 mins/1 hour) = 16 mph
.
This gives us our second equation (2):
m-c = 16
m = 16+c
.
Plug the above into equation 1 and solve for c:
m+c = 24
16+c+c = 24
16+2c = 24
2c = 8
c = 4 mph