The speed of a river current is 3 mph. If a boat travels 20 miles downstream in the same time that it takes to travel 10 miles​ upstream, find the speed of the boat in still water.

Answer 1

Since d=rt, t=d/r

Time upstream = Time downstream (Given in the problem)

Let x = speed of the boat in still water upstream the boat will be slower, so you subtract current. Downstream the boat going with the current will be faster so you add it.

10/(x-3) = 20/(x+3) Cross multiply

10(x+3) = 20(x-3) Distributive property

10x+30=20x-60 Subtract 10 from both sides

10x+30-10x=20x-60-10x Simplify

30=10x-60 Add 60 to both sides

30+60=10x-60+60 Simplify

90=10x Divide both sides by 10

90/10=10x/10

x=9 The speed of the boat in still water is 9 mph