Question

Speed of the boat in still water is 10 kmph.If it can travel 26 km down stream and 14 km upstream in the same time, find the speed of the stream.

Answer 1

Let the rate of the stream be x km/h. The boat's rate when the river speeds up the boat by adding its speed of x km/h to the boat's speed giving 10+x km/h. The boat's rate when the river slows the boat down and subtracts its speed of x km/h from the boat's speed giving 10-x km/h. Time = Distance/Rate Downstream time = (Downstream Distance)/rate = 26/(10+x) Upstream time = (Upstream Distance)/rate = 14/(10-x) Those times are equal. 26/(10+x) = 14/(10-x) Might as well divide both sides by 2 13/(10+x) = 7/(10-x) Cross-multiply: 13(10-x) = 7(10+x) 130-13x = 70+7x -20x = -60 x = 3 km/h