Determine the average speed of the current in a river if a boat moves at 20 miles/hour in still water and takes 3 hours to travel 78 miles downstream.

The speed of the current in a river is 6 miles per hour.

Step-by-step explanation:

Given:

A boat moves at 20 miles/hour in still water and takes 3 hours to travel 78 miles downstream.

Now, to determine the average speed of the current in river.

Let the speed of boat in still water be

Boat moves in still water at = 20 miles/hour

So,

And the speed of the stream be

So, speed of downstream =

Now, the speed of upstream =

As given:

Distance = 78 miles.

Time = 3 hours.

Speed of downstream =

Speed of downstream =

As speed of downstream is taken as

Thus,

Speed of downstream =

(As we see above  )

⇒

Subtracting both sides by 20 we get:

⇒

⇒

So, speed of the stream = 6 miles per hour.

Therefore, the speed of the current in a river is 6 miles per hour.