A man paddles a canoe in a long, straight section of a river. The canoe moves downstream with constant speed 4 m/s relative to the water. The river has a steady current of 2 m/s relative to the bank. The man's hat falls into the river. Seven minutes later, he notices that his hat is missing and immediately turns the canoe around, paddling upriver with the same constant speed of 4 m/s relative to the water. How long does it take the man to row back upriver to reclaim his hat

7 minutes

Explanation:

From the question, the flow of the river applies equally to both the hat and the canoe. The best way to approach this problem is to look at it from a perspective that follows the water, and ignores the bank.

Hence, the water and the hat are stationary, and the man paddles away from the hat and then paddles back.

Now, the hat is at rest and relative to the water and the canoe always travels at a speed of 4 m/s relative to the water.

We are told that it takes 7 minutes for the man to travel away from the hat.

Since he is travelling at a constant speed, it will therefore take same time of 7 minutes for him to return.

So, it will take 7 minutes for the man to row back upriver to reclaim his hat.