At 9am, ship B was 65 miles due east of another ship, A. Ship B was then sailing due west at 10 miles per hour, and A was sailing due south at 15 miles per hour. If they continue their respective courses, when will they be nearest one another?
15 sqrt 13 miles at 11 am
To find when ships A and B will be nearest to each other, we need to determine the time it takes for their paths to intersect.
Let's break down the problem step-by-step:
1. At 9 am, ship B was 65 miles directly east of ship A.
2. Ship B is sailing due west at a speed of 10 miles per hour.
3. Ship A is sailing due south at a speed of 15 miles per hour.
To solve this problem, we can set up an equation to represent the positions of the two ships at any given time t.
For ship B:
Distance_B = 65 miles - (10 miles/hour) * t
For ship A:
Distance_A = (15 miles/hour) * t
To find the time t when the distance between ship A and ship B is the smallest, we need to find the point when Distance_A = Distance_B.
Setting the two equations equal to each other:
(15 miles/hour) * t = 65 miles - (10 miles/hour) * t
Now, we can solve for t:
15t = 65 - 10t
25t = 65
t = 65/25
t = 2.6 hours
Therefore, it will take 2.6 hours for ships A and B to be nearest to each other.
To determine the exact time, we need to add this time to 9 am when they started:
9 am + 2.6 hours = 11:36 am
So, ships A and B will be nearest to each other at 11:36 am if they continue their respective courses.