A car was 1/2 mile in front of me as we traveled down a straight road. If it were going 60 mph and I was traveling at 65 mph, how long would it take for me to catch up to it? And how far would I have traveled?
Solution to the Problem:
The answer is: 6 minutes and 6.5 miles.Let x = distance traveled by the other car until I catch up to it.
Then x + 1/2 = distance traveled by me.
Since the other car is traveling at 60 mph, the time it will travel is x / 60.
Since I am traveling at 65 mph, the time I will travel is (x + .5) / 65.
Equate both times since we will have traveled the same amount of time when I catch up to the other car.
So, x / 60 = (x + .5) / 65.
Then, 65x = 60x + 30
and 5x = 30, so x = 6 miles.
The time elapsed is 6 / 60 = 1/10 hour or 6 minutes.
(Or you could have divided 6.5 by 65 to get the same answer).
The distance I would have traveled is x + .5 = 6 + .5 = 6.5 miles.
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