Question

Cole'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. Suppose they both set their 12 hour watches correctly at 9:00am on Monday. In how many days will their watches next show the correct time together? — days

Answer 1

36 days

Explanation:

Cole's watch runs fast. In 1 day, it gains an hour. So in 12 days, it gains 12 hours and is correct again.

We find the multiples of

Multiples of 12:

12, 24, 36, 48, 60, 72, 84

Note that

1 hour = 60 minutes

12 hours= x

Cross Multiply

x = 12 × 60

x = 720 minutes

Julio's watch also runs fast. In 1 day it gains 20 minutes.

Hence, 720 minutes/20

= 36

Therefore, to calculated how many days will their watches next show the correct time together we use LCM method

We find the Multiples of 12 and 36

Multiples of 12:

12, 24, 36, 48, 60

Multiples of 36:

36, 72, 108

Therefore, LCM = 36

The number of days that their watches next show the correct time together is 36 days