Boating Math Question

Question

The boat could sail at 5 times the speed of the current in the river. Thus, the boat could go 84 miles upstream in 4 hours more than it took to go 54 miles downstream. What was the speed of the boat in still water? 

Answer 1

Let x = the speed of the current, then 5x = speed of the boat

Let T_D = time to go downstream

Then,

(5x - x) = 84/(T_D + 4) and (5x + x) = 54/T_D

4x = 84/(T_D + 4) and 6x = 54/T_D

Solving for x, we find that x = 3

Therefore,

Boat Speed = 15 mph and Current Speed = 3 mph