A motorboat traveling with the current went 24 miles in 2 ho

A motorboat traveling with the current went 24 miles in 2 hours. Against the current, it took 3 hours to travel the same distance. Find the rate of the boat in calm water and the rate of the current.

Solution

Let the speed of the boat in calm water and the speed of the current be x mph and y mph respectively. Since distance = speed * time, we have 2* (x +y) = 24 or, x + y = 12...(1) and 3*(x -y) = 24 or, x - y = 8...(2). On adding the two equations, we get x + y +x - y = 12 + 8 or, 2x = 20 so that x = 20/2 = 10. Then, from the first equation, we get y = 12- x = 12-10 = 2. We can verify the result by checking with the given information. If the speed of the boat in calm water is 10mph and the speed of the water current is 2 mph, then the speeds of the boat, with the current, and against the current are 10 + 2 = 12mph and 10 - 2 = 8mph. Thus, with the current, in 2 hours, the boat will travel 12*2 = 24miles. also, against the current, in 3 hours, the boat will travel 3*8 = 24 miles. Thus, the speed of the boat in calm water is 10mph and the speed of the water current is 2 mph.