Ben was trying to sleep one night but there was too much noise around him. His clock ticked every 5 seconds, a tap was dripping every 16 seconds and his dog snored every 18 seconds. He noticed on his clock that all 3 things happened together at 8 p.m.
- At what time would all 3 things happen together again?
- How many times would all 3 things happen together again from 8 p.m. to 10 p.m.?
(a)
LCM of 5, 16 and 18 = 720
1 min = 60 s
720 s = 720 ÷ 60 = 12 min
12 min after 8 p.m. is 8:12 p.m.
(b)
From 8 p.m. to 10 p.m. = 2 h
1 h = 60 min
2 h = 2 x 60 = 120 min
Number of times all 3 things happened together
= 120 ÷ 12
= 10 times
Answer(s): (a) 8:12 p.m.; (b) 10