A motorboat moves 12 miles per hour in still water. It travels 23 miles upstream and 23 miles downstream in a total time of 24.0 hours. What is the speed of the current?

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Answer 1 · 2017-11-19T02:04:23

#11# miles in an hour

Let #x# (mile/h) the speed of the current.
The moterboat travels #12-x# miles in an hour upstream and #12+x# miles/h downstream.

Solve the following equation.
#23/(12-x) + 23/(12+x) =24#

Multiple both sides by #(12-x)(12+x)#:
#23(12+x)+23(12-x)=24(12-x)(12+x)#

Then,
#276+23x+276-23x=24(144-x^2)#
#552=3456-24x^2#
#24x^2=2904#
#x^2=121#
#x=+-11#

The speed of the current must be positive. #x=11# is appropriate.

A motorboat moves 12 miles per hour in still water. It travels 23 miles upstream and 23 miles downstream in a total time of 24.0 hours. What is the speed of the​ current?