Same Day Off?Date: 12/08/2002 at 22:41:27 From: Tabitha Mole Subject: Math word problems One person has every ninth day off and started on Sunday, and another person has every sixth day off and started on Monday. When will they both be off on the same day? I have tried to use a calendar to count out the days and could not get it to work out. I don't think they will ever be off on the same day. Date: 12/08/2002 at 23:17:54 From: Doctor Ian Subject: Re: Math word problems Hi Tabitha, Let's see how things start out: S M T W T F S | S M T W T F S | S M T W T F S Person 1 w w w w w w w w - w w w w w w w w - w w w Person 1 w w w w w - w w w w w - w w w w w - w w So it looks as if the first person has days 9, 18, 27, ..., 9*n, ... off, and the second person has off 7, 13, 19, ..., (1 + 6*m), ... So the question is: What are the smallest integer values of n and m for which 9n = 6m + 1 n = (6m + 1)/9 Now, in order for n to be an integer, (6m + 1) must be a multiple of 9. But let's think about that for a minute. The number 6m will _always_ be a multiple of 3, right? So the number (6m + 1) will _never_ be a multiple of 3, which means that it will never be a multiple of 9, either. So you're right - they never get the same day off! - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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