what is the speed of the boat?

Question

11. A motorboat can go 12 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 12 miles. Find the speed of the boat.

Answer 1

Going downstream12 miles in 20 minutes is 36mph. 12m/(1/3hr)=36mph

Going Upstream 12 miles in 30 minutes is 24mph. 12m/(1/2hr)=24mph

 

The speed going downstream is the speed of the boat plus the speed of the river, while the speed going upstream is the speed of the boat minus the speed of the river.

D=B+R

U=B-R

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U=Upstream       =36mph

D=Downstream   =24mph

B=Boat

R=River

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The difference in the speed upstream versus downstream is twice the speed of the river.

U-D=(B+R)-(B-R)

U-D=B+R-B+R

U-D=2*R

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U-D=36-24=12mph

12mph=2*R

R=6mph

The speed of the river is 6mph, or half the difference in speeds

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Then just plug the speed (along with the U or D value calculated in the first step) into either the U or the D equation

U=B-R

24mph=B-6mph

30mph=B

or...

D=B+R

36mph=B+6mph

30mph=B

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The speed of the boat is 30mph