Question

In a charity triathlon, Mark ran half the distance and swag a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was just starting to bike the remaining 17 miles. What was the total distance of the race?

Answer 1

68 miles

Explanation:

The total distance can be determined from the fractions.

Solution

Let d represent the total distance of the race.

The distance running is 1/2d. The distance swimming is 1/4d. The remaining distance is 17 miles.

Remaining = total distance - distance running - distance swimming

17 mi = d -1/2d -1/4d = 1/4d . . . . . . . . use known fractions

68 mi = d . . . . . . . multiply by 4

The total distance of the race is 68 miles.

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Additional comment

This would be a very difficult race. A typical "iron man" race has a swimming distance under 2.5 miles, less than 1/10 of the distance running. The biking distance is typically about 4 times the running distance of "only" 26 miles. An iron man race can take about 17 hours to complete.

This race has a 17-mile swimming segment, which would take a fast swimmer on the order of 8 hours, by itself. (This is 2.7 times the length of a "marathon" swim.) Here, the running distance is 34 miles, about 30% longer than a marathon.