Question 1198761: Linda and Deepti are walking and jogging on a circular trail. Linda can complete onecircuit in 30 minutes, and Deepti can complete the circuit in 42 minutes. If they bothstart at the same place at the same time, when will they be at the starting place at thesame time?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52832)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
30 = 6*5
42 = 6*7
GCF of 30 and 42 is 6, since this is the largest factor they have in common.
LCM of 30 and 42 is 30*42/GCF = 30*42/6 = 210
We can verify that with these lists of multiples.- multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
- multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, ...
I've marked the LCM in red.
This is the smallest common multiple.
The LCM is useful for problems such as this because Linda and Deepti will complete a circuit at the same time every 210 minutes.
Extra info:
210 minutes = 180 minutes + 30 minutes
210 minutes = (180/60 hours) + 30 minutes
210 minutes = 3 hours + 30 minutes
also,
210 minutes = (210/60) hours
210 minutes = 3.5 hours
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