strategic time out
Number Theory
Level
3
a watch , which gains uniformly , is 3 minutes slow at noon on monday and is 3 minute 48 seconds fast at 2 p.m. on the following monday. what time it was correct ???
2 p.m. on tuesday
3 p.m. on thursday
1 p.m. on friday
3 p.m. on saturday
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1 solution
By some calculations, we can show that the clock gains 2.4 seconds every hour ( i.e. 404/170 ) ...so it requires 75 (i.e. 180/2.4) hours to overcome the three minutes for which the clock is already lacking .. ! and that is achieved at 3 p.m. on Thursday.. after which it will again gain which is, for us, of no use.. !