Alvin paddled for 2 hours with a 8-km/h current to reach a campsite. The return trip against the same current took 10 hours. Find the speed of the boat in still water.

The speed of the boat in still water is 12km/h.

Explanation:

This is a relative motion problem. The boat is moving relative to the water, which is moving relative to the ground. We can express this with the formula:

Where is the speed of the boat relative to the ground, is the speed of the boat relative to the water, and is the speed of the water relative to the ground.

We have that and that, in the first trip and in the second trip , where x is the distance traveled. Also, in the first trip  and are positive and in the second one are negative (because the boat goes in opposite directions). So, using some mathematics, we can say that:

This means that the speed of the boat relative to the water is 12km/h. This is independent to the speed of water, so the speed of the boat in still water is 12km/h.

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