Bunuel wrote:
In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?
A. 4
B. 5
C. 6
D. 7
E. 8
We can let the speed of the faster person = 10 and that of the slower person = 6. Notice that the faster person will finish the race in 4800/10 = 480 seconds.
The faster person must overtake the slower person when he runs exactly 1 lap, 2 laps, etc. more than the slower person. Let t be the time it takes when the faster person overtake the slower person We can create the equations:
10t = 6t + 400 (for 1 lap), 10t = 6t + 800 (for 2 laps), etc.
Notice that none of the values of t can be more than 480 seconds, the time when the faster person finishes his race. Solving the first equation, we have:
4t = 400
t = 100
That is, it takes 100 seconds for the faster person to overtake the slower person by 1 lap.
Solving the second equation, we have:
4t = 800
t = 200
That is, it takes 200 seconds for the faster person to overtake the slower person by 2 laps.
We can see that the values of t are increasing by 100, so it will take 300 seconds for the faster person to overtake the slower person by 3 laps, 400 seconds by 4 laps. Since the next one will be 500 seconds and recall that t can’t be more than 480, then there are only 4 times when the faster person overtakes the slower person.
Answer: A
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