Posted by **Maria** on Monday, November 21, 2011 at 8:47pm.

At t=0, ship A is 12 miles due north of ship B. Ship A travels 12 miles/hour due south, while ship B travels 8 miles/hour due east.

a. Write a function for the distance between the two ships.

b. At what time are the two ships closest?

- Calculuss--Optimization -
**Reiny**, Monday, November 21, 2011 at 11:16pm
At a time of t after t=0 , the southward distance covered by A is 12t miles, and the distance covered by B is 8t

Let the distance between them be d

I see a right - angled triangle.

a) d^2 = (8t)^2 + (12-12t)^2

b)

dd/dt = 2(8t)(8) + 2(12-12t)(-12)

= 0 for a min d

128t -288 + 288t = 0

416t = 288

t = 288/416 = 9/13 = .6923

they will be closest at 9/13 hours

= .6923 hrs

= 41.5 minutes

check:

at t = .6923 , d = 6.65640

take a value of t slightly higher and lower than .3923

t = .69 , d = 6.65648 , a bit farther than at t = .6923

t = .70 , d = 6.657 , a bit farther than at t = .6923

My answer is correct

- Calculuss--Optimization -
**Maria**, Monday, November 21, 2011 at 11:58pm
Thank you so much!

I appreciate it!

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