Answered

Related rates fixed buoy? A boat passes a fixed buoy at 9

a.m. heading due west at 3 miles per hour. Another boat passes the same buoy at 10

a.m. heading due north at 5 miles per hour. How fast is the distance between the boats changing at 11:30

a.m.? I can't figure this out! I would appreciate all the help I can get! Thank you!

Verified Answer :

MissPhiladelphia

For the answer to the question above,  let coordinates of boat B at 10 am at the buoy be (0,0) 
then co-ordinates of boat A is (3,0) 

let dist. between A & B be z, then at time t hrs after 10 
z² = (3+3t)² +(5t)² = 34t² +18t +9, 
value 112.5 at t = 1.5 

2z.dz/dt = 234t +29 
dz/dt = (34t +9)/z 
= (34*1.5 + 9)/√112.5 
= 5.6569 mph 

SenpaiTrill

Hello there.

Related rates fixed buoy? A boat passes a fixed buoy at 9 
a.m. heading due west at 3 miles per hour. Another boat passes the same buoy at 10 
a.m. heading due north at 5 miles per hour. How fast is the distance between the boats changing at 11:30 
a.m.?

 5.6569 mph 

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