A boat takes 4 min. to cross a river 90m wide directly when there is no current & 5min. When there is current. find the velocity of the current.

With no river flow, the boat crosses the river at 90/4 = 22.5 meters/min.

With river flow, it's speed relative to water is the same as above, but it crosses at a speed of 90/5 = 18 m/min, relative to and perpendicular to the shore.
Consider the vector right triangle with sides of river speed, speed relative to shore, and speed relative to water.
If v is the river speed,
v^2 + 18^2 = 22.5^2
Solve for v.

To find the velocity of the current, we can set up a proportion based on the given information.

Let's assume that the speed of the boat in still water is represented by V (in meters per minute) and the velocity of the current is represented by C (also in meters per minute).

When there is no current, the boat takes 4 minutes to cross the river. In this case, the distance the boat travels is the width of the river, which is 90 meters. So, the speed of the boat in still water is equal to the distance divided by the time, which gives us V = 90 meters / 4 minutes.

When there is a current, the boat takes 5 minutes to cross the river. In this case, the effective distance the boat travels is the width of the river plus the distance carried downstream by the current. Since the current is pushing the boat downstream, the boat's effective velocity is the difference between the speed of the boat in still water and the velocity of the current. So, the effective velocity is V - C. Therefore, the effective distance is equal to the effective velocity multiplied by the time, which gives us (V - C) * 5.

Since the distance traveled is the same in both cases (90 meters), we can set up the following proportion:

90 / 4 = (V - C) / 5

To solve for C, let's cross multiply and solve for C:

90 * 5 = 4 * (V - C)
450 = 4V - 4C
4C = 4V - 450
C = (4V - 450) / 4
C = V - 112.5

Therefore, the velocity of the current is V - 112.5 meters per minute.