SOLUTION: 2. 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

Algebra ->  Systems-of-equations -> SOLUTION: 2. 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       Log On


   

Question 1186467: 2. 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 - 1.2t². The distance that the police
motorbike travels can be modeled by the equation d (t) = 4t² How long will
it take for the police motorbike to catch up to Ram?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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 - 1.2t². The distance that the police
motorbike travels can be modeled by the equation d (t) = 4t² How long will
it take for the police motorbike to catch up to Ram?
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Find t when the 2 distances are equal.
150+%2B+75t+-+1.2t%5E2+=+4t%5E2
5.2t%5E2+-+75t+-+150+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5.2x%5E2%2B-75x%2B-150+=+0) has the following solutons:

x%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=%28-75%29%5E2-4%2A5.2%2A-150=8745.

Discriminant d=8745 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--75%2B-sqrt%28+8745+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-75%29%2Bsqrt%28+8745+%29%29%2F2%5C5.2+=+16.2033369928893
x%5B2%5D+=+%28-%28-75%29-sqrt%28+8745+%29%29%2F2%5C5.2+=+-1.78026006981234

Quadratic expression 5.2x%5E2%2B-75x%2B-150 can be factored:
5.2x%5E2%2B-75x%2B-150+=+%28x-16.2033369928893%29%2A%28x--1.78026006981234%29
Again, the answer is: 16.2033369928893, -1.78026006981234. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5.2%2Ax%5E2%2B-75%2Ax%2B-150+%29

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Ignore the negative solution.
t =~ 16.20334 seconds
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