Question

A boat on a river travels downstream between 2 points 20 miles apart in 1 hour. It makes its return trip against the current and it takes 2 ½ hours. What are the speed of the boat and the speed of the current?

Answer 1

There are two unknown quantities that we have to find.  In order to work with them, we have to give them temporary names.  Lets call the speed of the boat ' B ', and lets call the speed of the current ' C ' .

-- "Downstream", the current is helping the boat.  The boat sails past the trees at a speed of (B + C).

(Distance) / (Speed) = Time

(20 miles) / (B + C) = 1 hour

Multiply each side by (B+C), then divide by 1 hr:  20 mi/1 hr = B + C

-- "Upstream" the boat is going against the current. It sails past the trees at a speed of (B - C).

(Distance) / (Speed) = Time

(20 miles) / (B - C) = 2.5 hours

Multiply each side by (B-C), then divide by 2.5 hr: 20 mi/2.5 hr = B - C

We're in good shape now. We have 2 equations in 2 unknowns:

B + C = 20

B - C =  8

Add the two equations, and you get 2B = 28. So B = 14 mph

Subtract the two equations and you get 2C = 12. So C = 6 mph

The speed of the boat is 14 mph .

The speed of the current is 6 mph .