A speed boat at the shore wants to overtake a sail boat that is 3 km out at sea. If the sail boat is travelling away from the shore at 1.5km/hr, how fast should the speed boat travel to overtake the sail boat in 5 minutes fro the shore?

3+1.5*5/60 = 5/60 * x

Maths

To calculate the speed required for the speed boat to overtake the sail boat, we need to consider the relative speed between the two boats.

First, let's convert the time of 5 minutes to hours. Since there are 60 minutes in an hour, 5 minutes is equal to 5/60 = 1/12 hour.

Now, let's calculate the distance covered by the sail boat in 1/12 hour. The sail boat is traveling at a speed of 1.5 km/hr, so in 1/12 hour, it covers a distance of (1.5 km/hr) * (1/12 hr) = 1/8 km.

Since the speed boat wants to overtake the sail boat when it is 3 km away, it needs to travel a distance of 3 km - 1/8 km = 23/8 km to catch up.

The time required for the speed boat to cover this distance depends on its speed. Let's call the speed of the speed boat S km/hr.

Using the formula distance = speed * time, we can rearrange it to find the time: time = distance / speed.

So, the time required for the speed boat to overtake the sail boat is (23/8 km) / S km/hr = (23/8) / S hr.

We know that this time should be equal to 1/12 hour (5 minutes). Therefore, we can set up the equation:

(23/8) / S = 1/12

To solve for S, we can cross multiply:

(23/8) * 12 = S

Simplifying further:

S = 34.5 km/hr

Therefore, the speed boat should travel at a speed of 34.5 km/hr to overtake the sail boat in 5 minutes from the shore.