Aptitude Day 256

Problems on Boats and Streams:

1. A motorboat, whose speed is 5 km/hr in still water goes 4 km downstream and comes back in a total of 2 hours 30 minutes. The speed of the stream (in km/hr):

Solution:

                  Let the speed of the stream be x.

                  4/(5+x) + 4/(5-x) 2(1/2)

                  4[(5-x+5+x)/25-x²] = 5/2

                  By solving the above equation, we get

                  x = 3 km/hr.

2. At his usual rowing rate, Sheldon can travel 120 miles downstream in a certain river in 60 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 240-mile trip, the downstream 120 miles would then take only 10 hours less than the upstream 120 miles. What’s the speed of the current in miles per hour?

Solution:

                  120/(u-v) – 120/(u+v) = 60

                  By solving the above equation, we get

                  4v+v² = u²------- Equation 1

                  120/(2u-v) – 120/(2u+v) = 10

                  By solving the above equation, we get

                  (24v+v² )/4= u²------- Equation 2

                  Equating 2 equations, we get

                  4v+v² = (24v+v² )/4

                  By solving the above equation, we get

                  v = 2(2/3) mph.