8. In a morning walk, three persons step off together. Their steps measure 70 cm, 75 cm and
80 cm respectively. What is the minimum distance each should walk so that all can cover
the same distance in complete steps?
9. The traffic lights at four different road crossings change after every 24 seconds,
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Step-by-step explanation:
8)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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9)Answer:
8.07.12 am
Step-by-step explanation:
Find the Prime Factors:
48 = 2⁴ x 3
72 = 2³ x 3²
108 = 2² x 3³
Find the LCM:
LCM = 2⁴ x 3³
LCM = 16 x 27 = 432
Convert 432 seconds to mins:
432 seconds = 432 ÷ 60 mins
432 seconds = 7.2 mins
7.2 mins = 7 mins 12 seconds
Find the time it will change together again:
8 am + 7 mins 12 seconds = 8.07.12 am
Answer: It will change together again at 8.07.12 am
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