Question

A committee organizing a marathon has 14 jugs of water and 20 jugs of sports drink. The committee would like to set up a number of refreshment stations along the marathon course, with the same combination of jugs of water and jugs of sports drink at each station, with no beverages left over. What is the greatest number of refreshment stations that can be set up?

Answer 1

2 stations with 7 of jugs of water and 10 of sports drink in each station

Explanation:

Lets start with the jugs of water, to have the same amount in each station you need have a number of station that divide for 14 the remainder or "left over" equal to 0, or in other words multiple of 14 in the interval 1 to 14

multiples of 14 : 1, 2, 7 and 14

so you can have

1 station with 14 jugs of water

2 stations with 7 jugs of water each

7 stations with 2 jugs of water each

14 station with 1 jugs of water each

Now we need to do the same for the 20 jugs of sports drink

multiple of 20 in the interval 1 to 20: 1,2,4,5,10 and 20

so you can have:

1 station with 20 jugs of sports drink

2 stations with 10 jugs of sports drink

4 stations with 5 jugs of sports drink

5 station with 4 jugs of sports drink

10 station with 2 jugs of sports drink

20 stations with 1 jugs of sports drink

So we have that both cases, water and sport drinks have coincidence of 1 or 2 stations, and the maximum of both is 2 stations with 7 jugs of water and 10 of sports drink each