Question

John rowed his boat against the current for 3 hours. The return trip with the current took 2 hours. What is Johns speed in still water if the speed of current is 2mph.

Not 13 or 4

Answer 1

John's speed is 10mph

Explanation:

Set the following:

Let

B = boat speed

C = current speed

Going upstream, the boat is travelling at its own speed, B, minus the speed of the opposing current, C

Upstream Speed = (B - C)

Upstream Time = 3 hours

Downstream Speed = (B + C)

Downstream Time = 2 hours

We will assume the distance to and from the destination is the same. We'll call it D.

Distance is the product of Time and Speed

Going Upstream D = (B - C)*(3 hr)

Going Downstream D = (B + C)*(2 hr)

Since D is the same, we can write:

(B - C)*(3 hr) = (B + C)*(2 hr)

3B - 3C = 2B +2C

B = 5C

Joh's boat is moving at 5 times the current speed.

The speed of the current, C, is 2mph.

B = 5*(2mph)

B = 10mph

Check:

Speed Upstream is (10 - C) or 8mph

Speed Downstream is (10+C) or 12mph

(8mph)*(3 hours) = 24 miles

(12mph)*(2 hours) = 24 miles