A speed boat at he 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 1.5 km/hr, how fast should the speed boat travel to overtake the sail boat in 5 minutes from the shore
After 5 minutes the sailboat will be
3 + 1.5((5/60) km or 3.125 km from shore
so the speed boat has to go 3.125 km in 5 minutes to catch it:
speed = distance/time
= 3.125/(5/60)
= 37.5 km/h
37.5KM/hr
To find out how fast the speed boat should travel to overtake the sail boat, we need to determine the relative distance between them and the time it takes for the speed boat to cover that distance.
Given:
- The sail boat is 3 km out at sea.
- The sail boat is traveling away from the shore at 1.5 km/hr.
- The desired time for the speed boat to overtake the sail boat is 5 minutes.
First, let's convert the 5 minutes into hours by dividing it by 60:
5 minutes = 5/60 = 1/12 hour
Next, we need to calculate how far the speed boat needs to travel to reach the sail boat. Since the sail boat continues to move away from the shore, we need to find the additional distance covered by the sail boat in 1/12 hour:
Additional distance = (1.5 km/hr) * (1/12) hr = 1.5/12 km
Now, we can calculate the total distance the speed boat needs to cover to overtake the sail boat:
Total distance = Distance between the boats + Additional distance
Total distance = 3 km + 1.5/12 km = 3 km + 0.125 km = 3.125 km
Lastly, to find the speed at which the speed boat needs to travel, we divide the total distance by the desired time:
Speed = Total distance / Time
Speed = 3.125 km / (1/12 hr)
Speed = 3.125 km * 12 = 37.5 km/hr
Therefore, the speed boat needs to travel at a speed of 37.5 km/hr to overtake the sail boat.