Question

The answer to all 11.

Answer 1

The rate of the current is 2 miles per hour.

Explanation:

Let us assume that the rate of the river is v miles per hour.

The speed of the boat is 12 miles per hour.

Let us assume also that the boat can go 21 miles in t hours in the downstream and 15 miles upstream at the same time i.e. t hours.

So, from the condition given we can write that

`12 + v = (21)/(t)` ......... (1), and

`12-v =(15)/(t)` ......... (2)

Now, adding those two equations we get

`24 = (21)/(t) +(15)/(t) = (36)/(t)`

⇒
`t = (3)/(2)` hours

Now, from equation (1), we get,

`12 + v = (21)/((3)/(2) ) =14`

⇒ v = 2 miles per hour

Therefore, the rate of the current is 2 miles per hour. (Answer)