January 29th, 2007, 01:32 PM  #1 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  The Clock
A clock gains 3 minutes every hour.If the clock is set correctly at midnight on January 1,when will it next show the correct time ?

January 29th, 2007, 02:43 PM  #2 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
If the clock gains 3 minutes every hour, then it gains time on a 1/20 ratio. We are interested in how long it will take it to gain 24 hours, which will happen after 480 hours, i.e, exactly 20 days. The clock will next show the correct time at midnight on January 21st. As time problems go, this one was pretty easy.

January 30th, 2007, 02:46 AM  #3 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
You said the clock will gain 24 hours after 480 hours = 20 days. Where in the question does it make it clear for me to know this data? 
January 30th, 2007, 02:47 AM  #4 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
The fact that it gains 3 minutes on the hour makes it clear.

January 30th, 2007, 02:52 AM  #5 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
3 minutes on the hour is the KEY PHRASE.

January 30th, 2007, 08:05 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,838 Thanks: 1564 
In this type of problem, it is usually intended that the clock gains or loses at a steady rate, which couldn't be true for a digital clock, but the wording is often unclear. There may also be ambiguity as to whether the clock distinguishes noon from midnight, 3am from 3pm, etc. If in doubt, state your assumptions or consider all possibilities.

January 30th, 2007, 01:07 PM  #7 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
Undoubtedly, the wording is very vague.

January 30th, 2007, 03:10 PM  #8 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
I assumed that it was a twentyfour hour clock (because that is what I generally use), but looking back on it, a twelvehour clock is more likely. This means that it would only take ten days rather than twenty, and would next be correct January 11.

February 2nd, 2007, 03:58 PM  #9 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
This would be a great weekend math question for high school kids.


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