robertops
Jeff and Ali race each other at the Tenleytown Speedway. Ali’s car travels at 300 feet per second, and Jeff’s car travels at 250 feet per second. If one lap around the track is 3000 feet long, and each car travels at a constant rate, how many laps will it take Ali to overtake Jeff?
(A) 1
(B) 5
(C) 6
(D) 10
(E) 60
Since a lap around the track is 3000 feet long, Ali’s rate in seconds per lap is 3000/300 = 10. Similarly, Jeff’s rate is 3000/250 = 12.
In order for Ali to overtake Jeff, she must travel one more lap than Jeff does. Thus, if we let p = the number of laps Jeff travels, p + 1 = the number of laps Ali travels. Since time = distance/rate, and when Ali overtakes Jeff, they will spend the same amount of time on the track, we have:
(p + 1)/12 = p/10
10(p + 1) = 12p
10p + 10 = 12p
10 = 2p
p = 5
We see that Jeff travels 5 laps. However, since Ali travels one more lap than Jeff, she travels 6 laps.
Alternate Solution:
We note that Ali overtakes Jeff precisely at the moment the distance covered by Ali is 3000 feet more than the distance covered by Jeff.
Since Ali’srate is 50 feet/sec more than Jeff’s rate, the distance between the two riders increases by 50 each second; thus, it takes 3000/50 = 60 seconds for Ali to overtake Jeff. It takes Ali 3000/300 = 10 seconds to complete a lap; therefore, it takes 60/10 = 6 laps for Ali to overtake Jeff.
Answer: C