Posted by eve on Sunday, July 31, 2011 at 7:32am.
A car is heading east toward an intersection at the rate of 40 mph. A truck is heading south, away from the same intersection at the rate of 60 mph. At what rate is the distance between the car and the truck changing when the car is 8 miles from the intersection and the truck is 15 from the intersection?

Math  Reiny, Sunday, July 31, 2011 at 10:01am
let's look at t hrs after the above condition
let the distance between them be D miles
then
D^2 = (40t+8)^2 + (15+60t)^2
2D dD/dt = 2(40t+8)(40) + 2(15+60t)(60)
dD/dt = [ 40(40t+8) + 60(15+60t) ]/D
when t = 0 , the above condition,
D = √8^2+15^2) = 17
and
dD/dt = [ 40(8) + 60(15) ]/17 = 71.76
At that moment they are separating at 71.8 mph
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