Multiples word problem: fast, correct watches being in synch

[KristinMC1]

Can anyone please help me with my 6th grade daughter's word problem we can't figure out?

Mario's watch runs fast. In 1 day it gains an hour; so in 12 days, it gains 12 hours and is correct again. Julio's watch also runs fast. In 1 day, it gains 20 minutes. If they both set their 12-hour watches correctly at 9:00 am on Monday, when will their watches both be correct again at the same time?

Somehow this problem is supposed to be solved by using multiples.

Thanks for any help. It is greatly appreciated!!!

 

[Deleted member 4993]

Re: Multiples word problem

Hi,
Can anyone please help me with my 6th grade daughter's word problem we can't figure out?

Mario's watch runs fast. In 1 day it gains an hour; so in 12 days, it gains 12 hours and is correct again. Julio's watch also runs fast. In 1 day, it gains 20 minutes. If they both set their 12-hour watches correctly at 9:00 am on Monday, when will their watches both be correct again at the same time?

Somehow this problem is supposed to be solved by using multiples.

Thanks for any help. It is greatly appreciated!!!

When would Julio's watch be correct again?

 

[jwpaine]

Re: Multiples word problem

Hi,
Can anyone please help me with my 6th grade daughter's word problem we can't figure out?

Mario's watch runs fast. In 1 day it gains an hour; so in 12 days, it gains 12 hours and is correct again. Julio's watch also runs fast. In 1 day, it gains 20 minutes. If they both set their 12-hour watches correctly at 9:00 am on Monday, when will their watches both be correct again at the same time?

Somehow this problem is supposed to be solved by using multiples.

Thanks for any help. It is greatly appreciated!!!

Mario: Every 24 hours it gains 1 hour:

Julio: Every 24 hours it gains 1/3 hour:

Watches start correctly at 9:00 am on Monday. After 12 days or 24(12) hours, we know that Mario's watch is 12 hours faster than when he first set it, because for every 24 hours, he gains 1 hour, so: (24(12) / 24) * 1 = 12 hours ahead and thus back to normal on a 12 hour clock. Julio gains (1/3) an hour for every 24 hours on the clock.

How much faster is Mario's watch than Julio's watch? We know that Mario's watch increases by 1 hour every 24 hours and Julio's watch increases by 20 min, therefor Mario's watch is 3x faster.

If we know that Mario's watch will be correct every 12 days, than Julie's watch will be correct at 3 * 12 days, and sense (3 * 12) is divisible by 12, Mario's watch will be equal to Julio's watch after 3 * 12 days after it was set at 9:00 am, on Monday

John

 

[KristinMC1]

Thank you so much!!!