Question

Two men a and b walk round a circle 1200 m in circumference. A walks at the rate of 150 m/min and b at 80 m/min. If both of them start at the same time from the same point and walk in the same direction, when will they be together again for the first time

Answer 1

we know time=distance/speed

t1=1200/150=8sec

t2=1200/80=15sec

now LCM of 8,15=120

so they will meet after 120 seconds

Answer 2

Two men be together again for the first time after 2 hours

Solution:

Two men a and b walk round a circle 1200 m in circumference

Distance = 1200 m

A walks at the rate of 150 m/min and b at 80 m/min

$Time = \frac{distance}{speed}$

Therefore,

$\frac{1200}{150} = 8\ minutes\\\\\frac{1200}{80} = 15\ minutes$

Find LCM of 8 and 15

List all prime factors for each number.

Prime Factorization of 8 is:  2 x 2 x 2

Prime Factorization of 15 is:  3 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 5 = 120

120 minutes = 2 hours

Thus they be together again for the first time after 2 hours

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