SOLUTION: The speed of a car was tracked by radar in a police helicopter over a period of 10 minutes. The police found that the car's speed could be represented by the equation: s = 3t squar

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Question 166463: The speed of a car was tracked by radar in a police helicopter over a period of 10 minutes. The police found that the car's speed could be represented by the equation: s = 3t squared - 30t + 135
where s is the speed of the car in kilometers per hour after t minutes have passed.
a. When was the car travelling at 80km/h?
b. When was the car travelling at 120km/h?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first part to get you started

a)

s+=+3t%5E2+-+30t+%2B+135 Start with the given equation


80+=+3t%5E2+-+30t+%2B+135 Plug in s=80


0+=+3t%5E2+-+30t+%2B+135-80 Subtract 80 from both sides.


0+=+3t%5E2+-+30t+%2B+55 Combine like terms.


Notice we have a quadratic equation in the form of at%5E2%2Bbt%2Bc where a=3, b=-30, and c=55


Let's use the quadratic formula to solve for t


t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


t+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-30, and c=55


t+=+%2830+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29 Negate -30 to get 30.


t+=+%2830+%2B-+sqrt%28+900-4%283%29%2855%29+%29%29%2F%282%283%29%29 Square -30 to get 900.


t+=+%2830+%2B-+sqrt%28+900-660+%29%29%2F%282%283%29%29 Multiply 4%283%29%2855%29 to get 660


t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%282%283%29%29 Subtract 660 from 900 to get 240


t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


t+=+%2830+%2B-+4%2Asqrt%2815%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29 or t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29 Break up the expression.


So the answers are t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29 or t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29


which approximate to t=7.582 or t=2.418

So the this means that at 2.418 seconds or at 7.582 seconds, the car was traveling at 80 km/h