Bus Station

Number Theory Level 1

At a bus station, bus #263 comes every 5 minutes, bus #145 comes every 7 minutes, and bus #259 comes every 9 minutes. At 9:00 am, the 3 buses arrived at the same time! When is the next time that all 3 will arrive together?

14:15 (2:15 pm) 12:30 15:50 (3:50 pm) 13:20 (1:20 pm)

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Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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2 solutions

LCM of 5,7 and 9 is 315 minutes i.e, 5 hrs 15 minutes(315/60=5.15) The buses will arrive in the station together after 3 hrs 15 minutes 0900+0315=1415. Hence, the answer is 14:15

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Could you explain why the buses would arrive together after 3 hrs 15 minutes instead of 5hrs and 15 mins?

Simran Shah - 6 years ago

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It is 5 hours and 15 minutes. It was a typo. If they added 3 hours and 15 min it would give 1215 but the answer given was 1415. What they meant to say was since the lowest common denominator is 315 (9×7×5) and 315/60 min= 5.25 hours (or 5 hours and 15 min), 0900+0500+0015=1415 (or 2:15 pm)

John Witter - 5 years, 7 months ago
Venture Hi
Feb 28, 2015

Lcm(5,7,9)=315

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