Question

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.

Answer 1

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

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
`x\ miles\ per\ hour.`

Boat moves in still water at = 20 miles/hour

So,
`x=20\ miles\ per\ hour.`

And the speed of the stream be
`y\ miles/hr.`

So, speed of downstream =
`(x+y)\ miles/hr`

Now, the speed of upstream =
`(x-y)\ miles/hr`

As given:

Distance = 78 miles.

Time = 3 hours.

Speed of downstream =
`(Distance)/(Time)`

Speed of downstream =
`(78)/(3)=26\ miles\ per\ hour`

As speed of downstream is taken as
`(x+y)\ miles/hr`

Thus,

Speed of downstream =
`(x+y)\ miles/hr`

`26=x+y`

(As we see above
`x=20\ miles\ per\ hour.`)

⇒
`26=20+y`

Subtracting both sides by 20 we get:

⇒
`6=y`

⇒
`y=6.`

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

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