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?

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.