Q. My husband's watch gains 2 minutes every watch and my watch loses 1 minute for each hour. One day, we were late to marriage because the difference between the time in the two watches was 1 hr and we looked at the slow watch. When did we last set our watches to the same time?

• 1st hr diff 3min 2nd hr 6min 3rd 9min so ap series 3,6,9,12...... diff 60min 60 is 20th term by applng frula of nth trm a+(n-1)d=60 whre d=3,a=3,n=? so they last set dr wtch before 20hr
• 11 years agoHelpfull: Yes(14) No(1)
• Suppose they had set their watches X hours ago.
  Husband's watch gains 2X/60 hour every hour while wife's watch loses X/60 every hour.
  
  Now as one watch gains and other loses the difference will be added
  
  Hence (2X/60) + (X/69)= 1 (hour)
  Thus X= 20 hours.
  Note : If both watches would have gained or if both would have been losing then we would have subtracted the difference.
• 9 years agoHelpfull: Yes(6) No(0)
• ans= 20 hrs
  
• 9 years agoHelpfull: Yes(1) No(0)
• Key Details:
  Your husband's watch gains 2 minutes every hour.
  Your watch loses 1 minute every hour.
  When you and your husband were late to the marriage, the difference between the time on your watches was 1 hour.
  You both looked at the slow watch (which is yours), meaning that your watch was showing a time that was 1 hour behind your husband's watch at that moment.
  Step-by-Step Solution:
  Let’s assume that both watches were set to the same time at some point in the past.
  
  Understanding the Watches’ Behavior:
  Your husband’s watch gains 2 minutes per hour. This means after
  𝑡
  t hours, his watch is ahead by
  2
  𝑡
  2t minutes.
  Your watch loses 1 minute per hour. This means after
  𝑡
  t hours, your watch is behind by
  𝑡
  t minutes.
  Time Difference Between the Watches:
  After
  𝑡
  t hours, the total difference between the two watches will be:
  Difference
  =
  (
  Time gain of husband’s watch
  )
  −
  (
  Time loss of your watch
  )
  Difference=(Time gain of husband’s watch)−(Time loss of your watch)
  Difference
  =
  2
  𝑡
  −
  𝑡
  =
  𝑡
  Difference=2t−t=t
  The time difference between the two watches is
  𝑡
  t minutes, where
  𝑡
  t is the number of hours that have passed since you both set your watches to the same time.
  Given Condition:
  The difference between the two watches is 1 hour, or 60 minutes.
  𝑡
  =
  60
   
  minutes
  =
  1
   
  hour
  t=60minutes=1hour
  Solving for
  𝑡
  t:
  We know that the time difference is 60 minutes, so:
  𝑡
  =
  60
  t=60
• 15 Days agoHelpfull: Yes(0) No(0)