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 acce

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Question 1120623: 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 ankor@dixie-net.com(22740) (Show Source):
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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?
:
the travel time of Ram and the cop will be the same therefore
4t^2 =-1.5t2 + 75t + 150
4t^2 +1.5t^2 - 75t - 150 = 0
5.5t^2 - 75t - 150 = 0
solve for t using the quadratic formula; a=5.5; b=-75; c=-150
The positive solution
t = 16.2 seconds
:
Graphing both equations

We can see they intersect at x=16