Question

A man wants to cross a river 500 m wide. His rowing speed (relative to the water) is 3000 m/h. The river flows at a speed of 2000 m/h. The man's walking speed on shore is 5000 m/h. (a) Find the path (combined rowing and walking) he should take to get to the point directly opposite his starting point in the shortest time. (b) How long does it take?"

Answer 1

To cross the river in the shortest time, the man should row diagonally across the river while also walking downstream. The total time taken to cross the river is 16 minutes.

Step-by-step explanation:

To find the path he should take to get to the point directly opposite his starting point in the shortest time, the man should row diagonally across the river while also walking downstream. This path will help him take advantage of both the rowing speed and the walking speed to minimize the total time taken.

The time taken to row across the river is equal to the distance across the river divided by the rowing speed. So, the time taken to row across the river is 500 m / 3000 m/h = 1/6 h = 10 minutes.

Similarly, the time taken to walk downstream is equal to the distance downstream divided by the walking speed. So, the time taken to walk downstream is 500 m / 5000 m/h = 1/10 h = 6 minutes.

Therefore, the total time taken to cross the river is 10 minutes (rowing) + 6 minutes (walking) = 16 minutes.