# Calculus

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Two trucks start from the same point. One truck travels due east at a rate of 50 mph and the other trucks travels due north at a rate of 60 mph. At what rate is the distance between the two vehicles increasing 1 1/2 hours later?

I think the answer is 55 mph because I added 60 + 55 and divided by 2 and got 55 mph.

• Calculus -

Oh my :(

The distance between them is the hypotenuse of a right triangle.

D^2 = x^2 + y^2
where
x = 50 t
y = 60 t
so
D^2 = 2500 t^2 + 3600 t^2 = 6100 t^2
now take time derivative

2 D dD/dt = 12200 t
at t = 1.5
D^2 = 6100 (2.25)
D = 117 miles
2 D = 234.3 miles
so
dD/dt = 12200(1.5)/234.3 = 78.1 miles/hour

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