A canoeist wishes to cross a river 0.5 km wide from A to B. If a current of 3 m/s flows and he is capable of paddling at 5 m/s in still water, how long does it take him to cross the river?

First, we need to find the velocity of the canoeist relative to the water.

The canoeist's velocity in still water is 5 m/s, and the current is flowing at 3 m/s. Since the current is flowing in the opposite direction of the canoeist's paddling, we subtract the current velocity from the paddling velocity to get the canoeist's velocity relative to the water:

5 m/s - 3 m/s = 2 m/s

Now, we can calculate the time it takes for the canoeist to cross the river using the formula:

Time = Distance / Velocity

The distance across the river is 0.5 km, which is equal to 500 meters. The canoeist's velocity relative to the water is 2 m/s. Plugging these values into the formula:

Time = 500 m / 2 m/s = 250 seconds

Therefore, it will take the canoeist 250 seconds, or 4 minutes and 10 seconds, to cross the river.

Step 1: Determine the effective paddling speed.

The canoeist's actual paddling speed is reduced by the current speed. So, the effective paddling speed is:

Effective paddling speed = Canoeing speed - Current speed
= 5 m/s - 3 m/s
= 2 m/s

Step 2: Calculate the time to cross the river.

Distance = Speed - Time
Time = Distance / Speed

In this case, the distance is 0.5 km, which is 500 meters, and the effective paddling speed is 2 m/s.

Time = 500 m / 2 m/s
= 250 seconds

Therefore, it takes the canoeist 250 seconds (or approximately 4 minutes and 10 seconds) to cross the river.