Question

The answer to all 11.

Answer 1

Answer:

The rate of the current is 2 miles per hour.

Step-by-step 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  

$12 + v = \frac{21}{t}$ ......... (1), and  

$12-v =\frac{15}{t}$ ......... (2)

Now, adding those two equations we get  

$24 = \frac{21}{t} +\frac{15}{t} = \frac{36}{t}$

⇒ $t = \frac{3}{2}$ hours

Now, from equation (1), we get,  

$12 + v = \frac{21}{\frac{3}{2} } =14$

⇒ v = 2 miles per hour

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