The Traveling Boat

Question

A boat traveled 75 miles downstream and back. The trip downstream took 4 hours. The trip back took 12 hours. Find the speed of the boat in still water and the speed of the current.

Answer 1

Let

V = speed of boat in still water

v = speed of water

D = RT

Downstream, the boat travels at speed V+v. To go 75 miles in 4 hours, it must average 75/4 = 18.75 mph

V + v = 18.75

Upstream, the boat travels at speed V-v. To go 75 miles in 12 hours, it must average 75/12 = 6.25 mph

V - v = 6.25

Adding these two equations yields:

2V = 25, or simply V = 12.5 mph

Subtracting instead yields:

2v = 12.5, or simply v = 6.25 mph