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Math Help - please help

  1. #1
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    please help

    A car traveling at a rate of 30 ft/sec is approaching an intersection. When the car is 120 ft from the intersection, a truck traveling at a rate of 40 ft/sec crosses the intersection. If the roads are at right angles to each other and the truck leaves the intersection after 2 seconds, how fast are the car and the truck separating when the truck leaves the intersection?
    a)4 ft/sec
    b)14 ft/sec
    c)50 ft/sec
    d)68 ft/sec
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  2. #2
    MHF Contributor
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    Ok. Draw a right triangle. Say a is the distance of the car from the intersection. Say b is the distance of the truck from the intersection, and say c is the distance between the car and the truck. You know the equality a^2+b^2=c^2 Good. Now differentiate and see what you can plug in. 2a\frac{da}{dt}+2b\frac{db}{dt}=2c\frac{dc}{dt} You know everything here but c, and dc/dt (which you are solving for) You can use right triangles to solve for c at t=2, and then you should have you answer.
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