A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.

hectictar
Sep 20, 2017

#1**+2 **

A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.

Distance / Rate = Time

Let the rate of the boat in still water = R

Against the current the rate of the boat = R - 2

With the current the rate of the boat = R + 2

So......equate the time

5 / ( R - 2) = 7 / ( R + 2) cross-multiply

5 ( R + 2) = 7 (R - 2) simplify

5R + 10 = 7R - 14 rearrange as

24 = 2R

12 = R = 12 mph

The time it takes = 5 / [12- 2] = 5 / 10 = 1/2 hr

CPhill
Sep 20, 2017