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29 Oct 2020, 10:38
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B
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A triathlon consists of three legs: a swim, a bike ride, and a run. A race organizer analyzes the results of a certain triathlon and observes that the ratio of swim distance to bike distance to run distance was 1 to 50 to 12, and that the ratio of average swim time to average bike time to average run time for all participants was 3 to 10 to 6. If the average speed of racers in each leg of the race does not change, but the race organizer changes the distance of each leg of the race so that the average swim time, average bike time, and average run time are now equal to each other, what fraction of the total distance of the race will be represented by the swim leg of the triathlon?
(A) 2/11
(B) 1/22
(C) 3/13
(D) 2/13
(E) 3/22
(A) 2/11
(B) 1/22
(C) 3/13
(D) 2/13
(E) 3/22
29 Oct 2020, 16:52
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Sajjad1994
The original average speed ratio is \(\frac{1}{3} : \frac{50}{10} : \frac{12}{6}\) which is 1/3: 5 : 2 or 1:15:6. The new distance is dependent on the new ratio of times, which is 1:1:1. Hence the new distance ratio is also 1:15:6. The swimming part is 1 out of 1 + 15 + 6 = 22 so the ratio is 1/22
Ans: 1/22.
General Discussion
05 Nov 2020, 11:43
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Sajjad1994
Solution:
We can let the distance, in miles, of swimming, biking, and running legs be 3, 150 and 36, respectively, and the time, in hours, to complete these legs be 3, 10 and 6, respectively. Therefore, the average speed, in mph, of these legs are 3/3 = 1, 150/10 = 15, and 36/6 = 6, respectively.
Notice that the total distance of the race is 3 + 150 + 36 = 189 miles. We can let x = the swimming leg distance, y = the biking leg distance, and 189 - x - y = the running leg distance. If we want the time for each leg to be the same, we want:
x/1 = y/15 = (189 - x - y)/6
For x/1 = y/15, we see that y = 15x. Now, setting x/1 = (189 - x - y)/6 and substituting 15x for y, we have:
x = (189 - x - 15x)/6
6x = 189 - 16x
22x = 189
x = 189/22
We see that the swimming leg distance is 189/22 miles, and therefore, the ratio of this distance to the distance of the entire race is (189/22)/189 = 1/22.
Answer: B
