7. Three persons start their morning walk from the same line at the same time and in the same
direction. Their steps measure 90 cm, 80 cm and 85 cm. At what distance from the starting line
will they be in the same line again?
Answers
GIVEN: Their steps measure 80 cm, 85 cm and 90 cm.
We have to find the L.C.M of the measures of their steps i.e. 80 cm, 85 cm, and 90 cm, to calculate the required distance each should walk.
L.C.M of 80 cm, 85 cm, and 90 cm.
80 = 2⁴ x 5
85 = 17 x 5
90 = 2 x 3 x 3 x 5
L.C.M of 80, 85 and 90 = 2⁴ x 3 x 3 x 5 x 17
L.C.M of 80, 85 and 90 = 12240 cm
Hence, the minimum distance each should walk so that all can cover the same distance in complete steps is 12240 cm.
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Given:
1st person steps = 90cm
2nd person steps = 80cm
3rd person steps = 85cm
Explanation:
We have to find the distance from the starting line when they will be in the same line.
So, we have to find LCM of 90, 80 and 85.
* Prime factorisation of 90 - 2 x 3 x 3 x 5
* Prime factorisation of 80 - 2 x 2 x 2 x 2 x 5
* Prime factorisation of 85 - 5 x 17
So, LCM = 2⁴ x 3² x 5 x 17 = 12240
Answer:
Therefore, they will be in the same line after walking 12240cm or 122m 40cm from the starting line.