SOLUTION: Ram is speeding along a highway when he sees a police motorbike parked on the side of the road right next to him. He immediately starts slowing down, but the police motorbike accel

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Question 1048636: Ram is speeding along a highway when he sees a police motorbike parked on the side of the road right next to him. He immediately starts slowing down, but the police motorbike accelerates to catch up with him. It is assumed that the two vehicles are going in the same direction in parallel paths.
The distance that Ram has traveled in meters 't' seconds after he starts to slow down is given by d(t)=150+75t-1.2t^2. The distance that the police motorbike travels can be modeled by the equation d(t)=4t^2. How long will it take for the police motorbike to catch up to Ram?
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
solve
4t%5E2=150%2B75t-1.2t%5E2
5.2t%5E2+-75t-150=0
t=144.4 secs
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 5.2t%5E2%2B-750t%2B-150+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-750%29%5E2-4%2A5.2%2A-150=565620.

Discriminant d=565620 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--750%2B-sqrt%28+565620+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-750%29%2Bsqrt%28+565620+%29%29%2F2%5C5.2+=+144.430492663918
t%5B2%5D+=+%28-%28-750%29-sqrt%28+565620+%29%29%2F2%5C5.2+=+-0.199723433148412

Quadratic expression 5.2t%5E2%2B-750t%2B-150 can be factored:
5.2t%5E2%2B-750t%2B-150+=+5.2%28t-144.430492663918%29%2A%28t--0.199723433148412%29
Again, the answer is: 144.430492663918, -0.199723433148412. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5.2%2Ax%5E2%2B-750%2Ax%2B-150+%29