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The faster car travels at a rate of 1/30 miles per second [2 miles in the track divided by 60 seconds to cover the track] and the slower car at a rate of 1/40 miles per second. The distance travelled by each car is it's speed multiplied by time. So let t = elapsed time.
So the distance covered by the faster car in t seconds is (1/30)t and the slower car is (1/40)t. The question is asking the amount of time taken for the faster car to be exactly one lap ahead of the slower car. This suggests that the distance covered by the faster car - the distance covered by the slower car is two miles (one lap). So you can make the equation
(1/30)t - (1/40)t = 2
and solve it for t.
You'll end up with t = 240 seconds. Which means that it takes 240 seconds (4 minutes) for the faster car to gain exactly one lap over the slower car.
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Math help!! (please!)



Math help!! (please!)
Two cars are driving around a two-mile track. One car makes a lap every 80 seconds, and the other other every 60 seconds. At these rates, how long will it take the faster car to gain exactly one lap on the slower car? How do I go about answering that?