Thread: World Problem Involving Derivatives

The World Problem:

At 9:30am, one ship was 65 miles due east from a second ship. If the first ship sailed west at 20 miles per hour and the second ship sailed southeast at 30 miles per hour, when were they closest together?

What I Have So Far:

1^st ship coordinates: (0,0)
2^nd ship coordinates: (-65,0)

x²+x²=(30t)²
x =

Letting time be 't' in hours since 9:30am :
1^st ship coordinates: (-20t,0)
2^nd ship coordinates: ( )

Not sure where to go where to go from here... Can anyone help me out?

If the distance between the two boats is then



For minimum differentiate this (no need to take the square root), and equate the result to zero.

So then would it be..





Which makes it 10:45am

Thank you so much for the guidance!!