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Math Help - The Shortest Time

  1. #1
    Newbie
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    The Shortest Time

    Jack, John and Jill go up the hill with five empty pails to a place where three springs are. Each of the five pails has an 8 litre capacity. One of the springs gives 2 litres of water in one minute while each of the other two gives 1 litre of water in one minute. It is impossible to use one spring to fill two pails at the same time, and it takes less than 2 minutes but more than 1 minute to take a pail from one spring to another one. What ist eh shortest time Jack, John and Jill need to fill all five pails to their capacity?

    Can someone please help? The answer 12 minutes is wrong, I have to find a shorter time.
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  2. #2
    Junior Member
    Joined
    Aug 2005
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    Try

    Hi,

    Let (1) be the spring which gives 2L a minute and (2) and (3) the other two.

    Suppose Jack puts a pail P1 at the spring (1) while John put another pail P2 at spring (2) and Jill put a pail P3 at sprint (3).

    After 3 minutes, Jack removes his pail P1 (it contains 6L) and put an empty one P4 at its place. He waits again 3 minutes and remove P4 (so P4 contains 6L) and puts the last pail P5 at its place.

    After 2 minutes (8 minutes have past from the beginning), John removes his pail (P2 which is full) and put P1 instead (which has 6L) and John removes his pail (P3 which is full) and put P4 instead (which has 6L). In these 2 minutes, Jack's pail P5 has 4L.

    We wait again 2 minutes and so, all pails are now full !!!

    So we have 10 minutes. (I didn't count the moving of P1 and P4 from spring 1 to the others because I assumed that it was done while the other were being filled (during their process)).
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  3. #3
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    Thank you very much!
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