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?

I got 2.4h for the captain heading east. I need to know how long the drifting will last. I don't know how to get that.

While "heading" east 2.4 hours at 50 km/h water speed, the boat will have also drifted 20*2.4 = 48 km north due to ocean current in that direction. It will therefore be only 60 - 48 = 12 km south of its destination after 2.4 hours. It only needs to drift with the current another

12 km/20km/h = 0.6 hours (36 minutes) to arrive.

Thanks for the help!

To determine the length of time for the drifting portion of the trip, we need to calculate the distance between the point due South of the destination and the destination itself.

Let's break down the problem step by step:

1. The boat is initially 120km West and 60km South of its destination.
2. It has to navigate through water with a current of 20km/h North. This means the boat will be pushed 20km/h North while it's drifting.
3. The captain decides to head the boat due East at 50km/h until he reaches a point due South of the destination.

To calculate the time taken for the captain to head East, we can use the formula:

Time = Distance / Speed

The distance the captain needs to cover heading East is 120km, and his speed is 50km/h. So:

Time = 120km / 50km/h = 2.4 hours

Now, let's determine the distance the boat will drift North during this time. The drift speed is 20km/h for 2.4 hours:

Distance drifted north = Speed x Time = 20km/h x 2.4 hours = 48km

At this point, the boat is in position due South (60km South of the destination) and has drifted 48km North. We need to find the remaining distance to the destination.

The boat started 120km West, drifted 48km North, and has to cover the remaining distance directly East to the destination. This forms a right-angled triangle.

Using the Pythagorean theorem, we can calculate the remaining distance (d):

d² = (120km)² + (60km - 48km)²
d² = 14400km² + 144km²
d² = 14544km²
d ≈ 120.54km

Now that we know the remaining distance is approximately 120.54km, we can calculate the drifting time using the speed of the boat while drifting, which is 20km/h:

Time = Distance / Speed = 120.54km / 20km/h ≈ 6.03 hours

Therefore, the drifting portion of the trip will last approximately 6.03 hours.