Question

in still water a boat averages 18 miles per hour. it takes the same amount of time to travel 4 miles downstream, with the current, as it does 2 miles upstream, against the current, what is the rate of the water current

Answer 1

The rate of water current = 6 mi / h

Explanation:

Speed of the boat in still water = u = 18 mi / h

Let Speed of the current = v

Now downstream speed is given by = u + v

And upstream speed is given by = u - v

Now time taken to travel 4 miles in downstream =
`(4)/(u + v)` ----------------------(1)

And time taken to travel 2 miles in upstream =
`(2)/(u - v)` ----------------------------(2)

Now from the question equation (1) = equation (2)

⇒
`(4)/(u + v)` =
`(2)/(u - v)`

⇒ 4 u - 4 v = 2 u + 2 v

⇒ 2 u = 6 v

⇒ u = 3 v

⇒ given that u = 18 mi / h

⇒ v =
`(18)/(3)`

⇒ v = 6 mi / h

Thus the rate of water current = 6 mi / h