Related Rates of Planes: Calculating Distance Change at Noon

[shanshan]

Homework Statement

At ten am, a plane traveling east at 100km/hr is 500 km west of a jet traveling south at 200km/hr. At what rate is the distance between them changing at noon?

Homework Equations

The Attempt at a Solution

2aa' + 2bb' = 2cc'
2(300)(-100) + 2(400)(200) = (1000)c'
-60000 + 160000 = 1000c'
c' = 1000 km/h

i need 186.1 km/h though.

 

[Mark44]

At noon, I find that the planes are moving apart at a rate of 100 km/hr at noon. I checked a couple of other times to see the rate at which the planes are moving apart. At 11am, the rate of change of distance was 0 km/hr. at 1pm, the rate of change of distance was about 158.1 km/hr. At 2pm, the rate of change is about 186.1 km/hr.

Are you sure you've given us the right times?

BTW, these are a couple of very slow planes. Many planes stall at speeds of 100km/hr, and a speed of 200km/hr for a jet is likewise very slow.

 

[shanshan]

yes, these are the times listed on my sheet. there may be a typo though.