Question

Garth can row 5 miles per hour in still water. It takes him as long to row 4 miles upstream as 16 miles

downstream. How fast is the current?

Answer 1

The speed of the current is 3 miles per hour

Explanation:

The equations for rate (r), distance (d), and time (t) are ⇒ d = rt, r = d/t, = t = d/r

Let x = speed in still water

Let c = speed of the current

The main difference with these problems is rate needs to be expressed using two variables because moving upstream the current is against you and downstream it moves with you.

Distance Rate Time

Upstream x − c

Downstream x + c

The distance column with the numbers from the problem and the value for speed in still water for x.

Distance Rate Time

Upstream 4 5 − c

Downstream 16 5 + c

The column for time using the other two columns knowing that rate, distance ⇒ time = Distance Rate Time

Upstream 4 5 − c

5 − c

4

Downstream 16 5 + c

5 + c

16

“It takes as long …” from the problem means that the two times are equal to each other. So, the equation can be written as:

4/5− c = 16/5 + c ⇒ Solve by cross-multiplying ⇒ 5(4 + c) = 16 5( − c) ⇒ c = 3