3. If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river a

Question

3. If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?

a. 7 &16 mph b. 7&17 c. 6 &17 mph d. 6 &18 e. none

Answer 1

b. 7 and 17

Answer 2

On the downstream run, the speed is 72/3 = 24 mph.

On the upstream run, the speed is 60/6 = 10 mph.

"Speed" as calculated above is composed of two parts, the first part being the speed of the boat in still water called Vb and the speed of the current called Vc.

So in the downstream run, Vb + Vc = 24

In the upstream run, Vb-Vc = 10

The sign of Vc is positive for downstream and negative for upstream since for the downstream case, the speed of the current helps you go faster.

So we have two equations and two unknowns:

Vb + Vc = 24

Vb - Vc = 10

Adding the equations eliminates Vc, leaving

2Vb = 34

Vb = 17 mph

Substituting Vb = 17 into any of the two equations, will give you Vc = 7 mph

So, the answer is 7,17

Answer 3

b. 7& 17