Question

A sight-seeing boat travels at an average speed of 21 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.6 miles downstream (with the current) in the same amount of time it takes to travel 2 miles upstream (against the current). Find the current of the river.

Answer 1

Explanation:

Let's call the speed of the boat in the river x miles per hour. The boat travels 2 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the water is the same in both directions. We can set up the following equation to represent this relationship:

21 - x = x + current speed

Solving for x, we find that the speed of the boat in the river is (21 - x)/2 = 10.5 miles per hour.

We can then use this value to find the current speed of the river. The boat travels 2.6 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the ground is the same in both directions. We can set up the following equation to represent this relationship:

10.5 + current speed = 10.5 - current speed

Solving for the current speed, we find that it is (10.5 - 10.5)/2 = 0.

Therefore, the current speed of the river is 0 miles per hour.