Question

Suppose that two boats leave a dock at different times. One heads due north, the other due east. Find the rate at which the distance between the boats is changing when the first boat is 34 miles from the dock traveling at a speed of 35 miles per hour and the second boat is 20 miles from the dock traveling at a speed of 43 miles per hour.

Answer 1

Let A represents the boat traveling north.

Let B represents the boat traveling east.

Let y be the distance b/w dock and boat A at any time t,

Let x be the distance b/w dock and boat B at any time t,

Let R be the distance b/w boats at any time t,

Using the Pythagorean theorem, we can write

diff wrt t,

I hope this answer helps,
Thanks,
Keep posting questions.