A grain barge travels on a river from point A to point B loa

A grain barge travels on a river from point A to point B loading and unloading grain. The barge travels at a rate of 7 mph relative to the water. The river flows downstream at a rate of 1 mph. If the trip upstream takes 2 hours longer than the trip downstream, how far is it from point A to point B?

Solution

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

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

Speed upstream = (u - v) km/hr.

u = 7mph ; v = 1 mph

u +v = 8 mph ; u -v = 6 mph

distance between A and B = d

d/8 +2 = d/6

d( 1/8 - 1/6) = -2

d(-2/16) = -2

d = 16 miles