A motorboatcan go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the cutrent.

Let m = speed of motorboat

and c = speed of current

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When going downstream, current speed is added to boat speed - - and, the total speed is "8 miles downstream in 20 minutes"

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To convert to "miles per hour" we multiply by 60 mins per 1 hour:

(8 miles/20 mins) * (60 mins/1 hour) = 24 mph

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This gives us our first equation (1):

m+c = 24

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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

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This gives us our second equation (2):

m-c = 16

m = 16+c

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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