Question

Mario's watch runs fast. In one day, it gains an hour. So in twelve days it gains 12 hours and is correct again. Julio's watch also runs fast. In one day it gains twenty minutes. Suppose they both set their 12 hour watches correctly at 9:00 a.m. on Monday. When will their watches next show the correct time together.

Answer 1

Given is that Mario's watch is correct every 12 days, so it is right on day 12, 24, 36, 48, 60, 72, 84...

Also given that Julio's watch gains 20 minutes each day, that means for his watch to gain 12 hours and be right again we will divide 720 minutes by 20.

12 hours = 720 minutes

So,
`(720)/(20)=36`

Therefore, every 36 days, Julio's watch is right, so it is right on day 36, 72....

The common 1st day between both is 36th day. The next is 72.

Hence, their watches will next show the correct time together on 36th day at 9:00 A.M. It will be a Tuesday at 9:00 A.M.

Answer 2

it takes Julio three times as long to gain as much extra time as Mario. So every 12 days Mario's click starts over at 9am. In 12 days, Julio will have only gained 4 hours. Julio needs to go 36 days to gain 12 hours. After 36 days both will be back at 9 am.