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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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