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?

Correct answer marked below

2/11

1/22

Correct

3/13

2/13

3/22

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Explanation

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Official Explanation

Official

The original average speed ratio is

\frac{1}{3} : \frac{50}{10} : \frac{12}{6}

which is

\frac{1}{3} : 5 : 2

1 : 15 : 6

.

The new distance is dependent on the new ratio of times, which is

1 : 1 : 1

.…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.