Sheila can row a boat 2 MPH in still water. How fast is the current of a river if she takes the same length of time to row 4 miles upstream as she does to row 10 miles downstream?

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Answer 1 · 2016-06-30T16:56:07

The speed of current of river is #6/7# miles per hour.

Let the current of water be #x# miles per hour and that Sheila takes #t# hours for each way. As she can row a boat at #2# miles per hour,

the speed of boat upstream will be #(2-x)# miles per hour and covers #4# miles hence for upstream we will have

#(2-x)xxt=4# or #t=4/(2-x)#

and as the speed of boat downstream will be #(2+x)# miles per hour and covers #10# miles hence for upstream we will have

#(2+x)xxt=10# or #t=10/(2+x)#

Hence #4/(2-x)=10/(2+x)# or #8+4x=20-10x#

or #14x=20-8=12# and hence #x=12/14=6/7# and #t=4/(2-6/7)=4/(8/7)=4xx7/8=7/2# hours.