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
[tex]12 + v = \frac{21}{t}[/tex] ......... (1), and
[tex]12-v =\frac{15}{t}[/tex] ......... (2)
Now, adding those two equations we get
[tex]24 = \frac{21}{t} +\frac{15}{t} = \frac{36}{t}[/tex]
⇒ [tex]t = \frac{3}{2}[/tex] hours
Now, from equation (1), we get,
[tex]12 + v = \frac{21}{\frac{3}{2} } =14[/tex]
⇒ v = 2 miles per hour
Therefore, the rate of the current is 2 miles per hour. (Answer)
