a boat leaves a doct at 2:00pm, heading west at 15km/h. Another boat heads south at 12km/h and reaches the same dock at 3:00pm. When were the boats closest to each other.
To find out when the boats were closest to each other, we need to determine their positions at different times and calculate the distance between them.
Let's assume the boat heading west left the dock at point A, and the boat heading south arrived at the dock at point B. Point A would be the starting point for the westbound boat, and Point B would be the destination point for the southbound boat.
Now, let's break down the problem into smaller steps:
1. Determine the position of the westbound boat at different times:
- The westbound boat started at 2:00 pm and traveled west at a speed of 15 km/h. Therefore, its position can be determined using the formula: distance = speed × time.
- At 2:00 pm, the westbound boat has traveled 0 km.
- At 3:00 pm, the westbound boat has traveled for 1 hour at a speed of 15 km/h, so its position would be 15 km west of the dock.
2. Determine the position of the southbound boat at different times:
- The southbound boat arrived at 3:00 pm, so we can determine its position just before it arrived at the dock.
- The speed of the southbound boat is 12 km/h, and the travel time is 1 hour. Using the same formula as before, we can calculate the distance: distance = speed × time.
- At 3:00 pm, just before reaching the dock, the southbound boat would be 12 km south of the dock.
3. Calculate the distance between the boats at different times:
- To calculate the distance between two points, we can use the distance formula: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
- At 2:00 pm, the distance between the two boats would be √((0 - 0)^2 + (12 - 0)^2) = 12 km.
- At 3:00 pm, the distance between the two boats would be √((15 - 0)^2 + (12 - 12)^2) = 15 km.
Based on these calculations, we can see that the boats were closest to each other at 2:00 pm when they are 12 km apart.