Using an Ordered List To Solve Problems

James and Ronald want to go visit their grandmother who lives in a neighboring city.  James and Ronald both work full-time.  James works three days straight, and gets every fourth day off.  Ronald works every fours days, and gets every fight day off.  James and Ronald want to discover a few possible days where they could make a trip to visit their grandmother together.

How can we do this?

Lets try to solve this by making a list of multiples, and comparing them to see if we can find common multiples.  

 

James gets every 4th day off.  So lets when he will have time off.

4, 8, 12,16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 52, 60 (each of these numbers represents how many days from now he will have a day off)

Ronald gets every fifth day off.  So lets see when he will have time off.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65

If we look at both lists, we see a few numbers that they have in common.

20, 40, 60.

We know that twenty days from now Ronald and James will  both have the day off.

We know that forty days from now Ronald and James will both have the day off.

We know that sixty days from now, Ronald and James will both have the day off.

Therefore, Ronald and James could choose to visit their grandmother together in 20, 40, or 60 days.

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