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Peggy competes in a biathlon by running and bicycling around a large loop through a city. She runs the loop one time and bicycles the loop five times. She can run 7 mph and she can ride . If the total time it takes her to complete the race is , determine the distance of the loop.

Sagot :

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The distance of the loop is 6 miles

Given that :

Running speed = 7 mph

Number of times she ran the loop = 1

Biking speed = 14 mph

Number of times she biked the loop = 5

Total time taken to complete the race = 3 hours

Recall :

Speed = distance / time

Speed = distance / time Time = distance / speed

Let the loop distance = d

Time taken to run 1 time : d / 7 hours

Time taken to bike 5 times = 5(d / 14) hours

Total time taken :

3 = (d/7) + (5d/14)

L. C. M of 7 and 14 = 14

3 = (2d + 5d) / 14

Multiply both sides by 14

14 × 3 = 2d + 5d

42 = 7d

d = 42 / 7

d = 6

Hence, the distance of the loop in miles is 6 miles

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