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A gas station stands at the intersection of a north-south road and an east-west road. A police car is traveling towards the gas station from the east, chasing a stolen truck which is traveling north away from the gas station. The speed of the police car is 100 mph when it is 3 miles from the gas station. At the same time the truck is 4 miles from the gas station going 80 mph. At this moment:

a. Is the distance between the car and the truck increasing or decreasing? How fast?
b. Repeat part a) if the truck is going 70 mph instead of 80 mph

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2 answers

  1. a = distance apart = (x^2 + y^2)^.5
    at present a = 5 miles (3,4,5 triangle)

    da/dt = .5 (x^2+y^2)^-.5 (2x dx/dt + 2 y dy/dt)
    if dx/dt = -100
    dy/dt = +80
    then
    da/dt = (.5/5)(2*3*-100 + 2*4*80)
    = (.1)(-600 + 640)
    = +4
    the truck is making a getaway at the moment.
    You can do it for the truck doing 70 mph. I suspect the truck will be losing then.

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  2. SO B is -4. which is decreasng

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