Expert: Chanda Walker - 4/24/2009

Question
Two cars are driving around a two-mile track. One car makes a lap every
eighty seconds. The other car makes a lap every sixty seconds. At these rates,
how long will it take the faster car to gain a lap on the slower car?

For this problem I subtracted 80-60=20 seconds to find the difference
between the two drivers. Then I divided 60/20=3 to find out how many 20
second intervals are added onto the slower driver's time every lap. I don't
know if I worded that correctly. Lastly, I multiplied the faster driver's time by
how many laps that need to be run in order to lapse the slower driver
(80x3=240 seconds). Could you tell me if I solved this question correctly and
if so did my explanation make sense?

Answer
You need to covert from seconds to speed.

speed = distance/time
speed1 = 1/80 laps/second
speed2 = 1/60 laps/second

The distance traveled is

speed*time

So

car1 = 1/80* time  (in units of laps)
car2 = 1/60* time

We want to know when car2 will have traveled one lap more than car1 in the same length of time.

Here is the equation:

1/80 * time + 1 = 1/60 * time

Now just solve for time.

(1/80 - 1/60)* time = -1
(60 - 80)/2400 * time = -1
time = 2400/20
time = 120 seconds

Let me know if I can help further.