Time for the 2 buses to leave a station the same time

[mariarenila]

Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9.00 am.

When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

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I tried doing it manually like this ...

Acton (every 24 mins) Barton (every 20 mins)
9.00 9.00
9.24 9.20
9.48 9.40
10.12 10.00

I can't think of a Maths concept to go thru time progression till it hit the same time.

Any help will be appreciated please ....

Many thanks,
Maria

 

[Mrspi]

Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9.00 am.

When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

**************************************************************************

I tried doing it manually like this ...

Acton (every 24 mins) Barton (every 20 mins)
9.00 9.00
9.24 9.20
9.48 9.40
10.12 10.00

I can't think of a Maths concept to go thru time progression till it hit the same time.

Any help will be appreciated please ....

Many thanks,
Maria

You want to look for a number of minutes that is a multiple of 24 (for bus A) and ALSO a multiple of 20 (for bus B). The smallest such number (the LEAST COMMON MULTIPLE) will tell you the number of minutes it will be after 9 a.m. when the two leave at the same time next. You will have to ADD that number of minutes to 9:00 a.m. to know the TIME at which they will next leave simultaneously.

The method you have started to use will surely work, but you just need to continue it further....until you get to the first common departure time after 9 a.m.

 

[Deleted member 4993]

I suggest you follow Mrsπ's suggestion and use LCM to do these types of problem.

Like she said - you can do it by your way but it might take a longtime to get to the common time.

Suppose you are doing the same problem with a third bus leaving every 35 minutes. Now the common-time will come every 840 minutes. With LCM you can solve it one line - other method will take way longer.

 

[HallsofIvy]

Look at prime divisors: 20= (2)(2)(5) and 24= (2)(2)(2)(3). Their "least common multiple" must include all those primes so is (2)(2)(2)(3)(5).