Math CentralQuandaries & Queries



Question from Ms., a parent:

Car 1 is traveling down the road at 50 mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1?

Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question?
Befuddled Mom?


The only formula I used in approaching this problem is that rate is distance divided by time.

Car 1 travels a short distance in the 10 second wait and then it takes a certain amount of time to travel from where it is to the half mile mark. Car two then has to travel one half mile in that time. The question is, at what speed must car 2 travel to accomplish this.

First I have to know how far car 1 travels in 10 seconds at 50 mph.

\[10 \mbox{ seconds} = 10 \mbox{ seconds} \times \frac{1}{60} \frac{\mbox{minutes}}{\mbox{ seconds}} \times \frac{1}{60} \frac{\mbox{hours}}{\mbox{ minutes}} =\frac{1}{360} \mbox{hours.}\]

At 50 mph how far does car 1 travel in that time? How much further does car 1 need to travel to reach the half mile marker? How many hours will that take at 50 mph? At what speed does car 2 need to travel to go one half mile in that amount of time?


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