A boat takes 3.0 h to travel 27 km down a river, then 6.0 h to return. How fast is the river flowing in km?

Answer 1

A boat takes 3.0 hours to travel down a river and 6.0 hours to travel back up. The distance is 27 km.

How fast is the river flowing?

This problem is asking to determine how fast the river is flowing. It's looking for rate.

Let C=rate of the current

Let B=rate of the boat.

--------------------------> Down river, the boat is traveling in the same direction as the current (It takes less time to travel with the current)

<-------------------------- Upriver, the boat is traveling in the opposite direction as the current.

The distance traveled is the same in both directions. The time traveled is different.

distance = rate x time.

For upriver.. The rate of travel would be the rate of the boat plus the rate of the current

27km = (B + C) x 3hr

For downriver. The rate of travel would be the rate of the boat minus the rate of the current.

27km = (B-C) x 6hr.

This gives us a systems of equations that we can now solve and determine the rate of the river current.

27km = 3(B+C)

9km = B + C

9km - C = B

27km = (B-C) x 6hr

27/6 = B-C

27/6 + C = B

Now we can substitute equation 1 into equation 2

27/6 + C = 9-C

2C = 9-27/6

2C=4.5

C = 2.25km/hr.

So the river Current = 2.25km/Hr.

The Boat would then be

27/6 + C = B

6.75km/hr = B

We can check to verify our answers are correct.

27 = 3(B+C)

27 ? 3(6.75 +2.25)

27 ? 27 (This works)

27 = (B-C) x 6hr

27 ? (6.75-2.25)6

27 ? 27 (This is correct)

So the river was flowing downstream at 2.25 km/hr