One watch is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 am on Friday. When did it show that correct time?

Question

(1) 5:00 am on Wednesday
(2) 5:00 pm on Wednesday
(3) 9:00 am on Wednesday
(4) 9:00 pm on Wednesday

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Answer 1 · 2018-08-10T02:21:45

(3) 9:00am Wednesday

The correct time will be shown when the watch has gained 1 minute.
We are told that the watch gains 3 minutes between 1pm Tuesday and 1am Friday.

First let's convert the time duration to minutes.

1pm Tuesday to 1pm Thursday is 2 full days #= 2*24#hr

1pm Thursday to 1am Friday is 12hr

Total time #= 48+12 = 60hr = 60*60 = 3600 min#

So the watch gains #3min "per " 3600 min#

But we only want 1 min gain for the watch time to be correct.

This will happen after #3600/3= 1200min#

Let's convert this back to hours and minutes so we can add it to the start time, to find the time that the watch shows the correct time.

#(1200min)/(60min/(hr)) = 20 hr#

1pm Tues #+ 20hr = (#1pm Wed #- 4hr) = 9#am Wednesday