A paddleboat can travel 60 miles upstream in the same time i

A paddleboat can travel 60 miles upstream in the same time it takes to travel 140 miles downstream. If the current of the river is 10 miles per hour, what is the speed of the paddleboat in still water?

Solution

Let the speed of the boat be x mph
Speed of river = 10 mph
Relative speed upstream = (x-10) mph
Distance covered upstream = 60
So time taken = distance/speed
= 60/(x-10) hrs
Relative speed downstream = (x+10) mph
Distance covered = 140 miles
Time taken = 140/(x+10) hrs
==> 140/(x+ 10) = 60/(x-10)
==> 140(x-10) = 60(x+10)
==> 140 x - 1400 = 60x +600
==> 140x - 60x = 600 + 1400
==> 80x = 2000
==> 80x/80 = 2000/80
==> x = 25
So speed of the boat = 25 mph