# SOLUTION: A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. The river flows at 2 miles per hours. What is the speed of the boat in still water?

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 Question 13650: A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. The river flows at 2 miles per hours. What is the speed of the boat in still water?Answer by atif.muhammad(135)   (Show Source): You can put this solution on YOUR website!```speed of boat in still water = x upstream speed = (x-2) --> it is slowed by 2 mph due to the flow of the river upsteam downstream speed = (x+2) --> it is speed up by 2mph due to the flow of the river downstream upstream distance = 5 miles downstream distance = 7 miles time to go upstream = distance/speed = 5/(x-2) time to go downstream = distance/speed = 7/(x+2) Now both the times to go upstream and downstream are the same therefore: 5/(x-2) = 7/(x+2) cross multiply the equation in order to get a common denominator: 5(x+2)/[(x-2)(x+2)] = 7(x-2)/[(x+2)(x-2)] we can forget about the denominator now as both sides of our equation have the same denominator. 5(x+2) = 7(x-2) multiply out the brackets 5x + 10 = 7x - 14 subtract 10 from both sides: 5x + 10 - 10 = 7x - 14 - 10 5x = 7x - 24 subtract 7x from both sides: 5x - 7x = 7x -24 -7x - 2x = - 24 2x = 24 x = 12 Therefore, the speed of the boat in still water is 12mph. It is 12mph as it is not affected by any current due to it being in still water. ```