The current in a stream moves at a speed of 3 miles per hour

The current in a stream moves at a speed of 3 miles per hour. A boat travels 5mi upstream and 5mi downstream in a total time of 2 hours. What is the speed of the boat in still water?

Solution

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

v = 3 mi/hr

Speed downstream = (u + v) km/hr.

Speed upstream = (u - v) km/hr

total time = 2hrs

5/(u+v) + 5/(u -v) = 2

5/( u +3) +5/( u -3) =2

5 [ 2u]/(u^2 -9) = 2

5u = u^2 -9

u^2 -5u -9 =0

u = 6.4 ; u = -1.4

neglect the -ve root

on solving the quadratic we get u = 6.4 mi/hr

speed of boat in still water , u = 6.4mi/hr