Question

At noon, ship A is 20 miles due west of ship B. Ship A is sailing west at 24 mph and ship B is sailing north at 23 mph. How fast (in mph) is the distance between the ships changing at 3 PM?

Answer 1

Hello,

I don't know how you solve this,
this is my resolution:

Let's e = the distance (in miles) between the 2 ships in function of t(time in hour)


`e= √((20+24*t)^2+(23*t)^2) =√(1105t^2+960t+400)\\\\ v=(de)/(dt) = (2*1105*t+960)/(2* √(1105*t^2+960*t+400)) \\\\ if\ t=15\ then\ v=(2*1105*15+960)/(2*√(1105*15^2+960*15+400)) \\\\ =33.22945583.... ( (mi)/(h) )`

Answer 2

The distance between the ships changing at 3 PM is 33 mph fast. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.