A boat is at a point 120km West and 60km South of its destination. It sails in water which has a current of 20km/h North. In order to arrive at the destination, the captain decides to head the boat due east at 50km/h until he reaches a point due South of the destination. He would then let the boat drift towards the destination. For what length of time should each portion of the trip last?
To solve this problem, we need to break down the boat's journey into two parts: the first part, where the boat heads due east at 50 km/h, and the second part, where the boat drifts towards the destination.
Let's first calculate the time it takes for the boat to reach the point due South of the destination by heading due east at 50 km/h.
The boat is initially 120 km west of the destination. Since the boat travels due east at 50 km/h, we can use the formula `time = distance / speed` to find the time it takes to travel this distance.
Time = 120 km / 50 km/h
Time = 2.4 hours
Now, let's calculate the distance the boat would drift in the 2.4 hours it takes to reach the point due South of the destination.
The boat's initial position is 60 km south of the destination, and there is a current of 20 km/h moving north. This means the boat drifts towards the destination at a speed of 20 km/h.
Distance drifted = speed × time
Distance drifted = 20 km/h × 2.4 hours
Distance drifted = 48 km
Therefore, the boat would drift approximately 48 km towards the destination in the 2.4 hours it takes to reach the point due South of the destination.
To find the length of each portion of the trip, the first part (heading due east) lasts 2.4 hours, and the second part (drifting towards the destination) lasts the same amount of time, 2.4 hours.
So, each portion of the trip should last 2.4 hours.