SOLUTION: If a car is going 85mph in 4.5 miles how fast would a stopped car have to go to catch up.

Question 628336: If a car is going 85mph in 4.5 miles how fast would a stopped car have to go to catch up.
Found 2 solutions by Alan3354, MrLarame:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If a car is going 85mph in 4.5 miles how fast would a stopped car have to go to catch up.
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"going 85mph in 4.5 miles" not clear what that means.
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Any speed >85 mi/hr would work. The time would depend on the speed.
Answer by MrLarame(2) (Show Source): You can put this solution on YOUR website!
I assume you mean that the car travelling at 85 mph can only cover 4.5 miles before the stopped car catches it?
In that case:
85mph = 1.25 mi per minute (85 / 60)
Since Distance = Rate * Time, we can say: 4.5mi = x mins * 1.25 mi/min, and solve for "x" by dividing both sides by 1.25mi/min:
(4.5mi) / (1.25mi/min) = (3.6 mins)
So the stopped car needs to accelerate fast enough that it can go the same distance in 3:36 minutes as the car already travelling at 80mph does.
How fast that is would depend on the acceleration of the stopped car.
If it could accelerate instantly, it would only need to go 85.0000001 mph! (or any other speed greater than 85)
If we assume it is a state patrolman with an interceptor, and he can accelerate to 90mph in 15secs, then he'd still have 3:26 to make up the 10 secs worth of distance you went in the meantime (apx 1/3 mile).
Since he'd be catching up by 5miles each hour, that would be 5/60 or 1/12 mile per minute, so it would take apx 4 mins to make up the 1/3 mile.
Sounds like he'd probably need to drive apx 95 mph, assuming he "got on it" right away.
There are a lot of variables here though that are not being taken into account, so this is just an "educated guess!"
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