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Math Help - Nice Question

  1. #1
    Member classicstrings's Avatar
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    Nice Question

    I'm not sure if this can be said to be a trick question... but maybe.

    Jack, John and Jill go up the hill with five 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 is the shortest time Jack, John and Jill need to fill all five pails to their capacity?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by classicstrings View Post
    I'm not sure if this can be said to be a trick question... but maybe.

    Jack, John and Jill go up the hill with five 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 is the shortest time Jack, John and Jill need to fill all five pails to their capacity?
    Take 3 buckets to the fast spring and 2 to the slow spring. Start filling.

    When the first bucket at the slow spring has X ltrs in it move it to the fast
    spring and start filling the other backet at the slow spring. Then as both
    springs are fully occupied the transit time does not add to the total fill time.

    Choose X so both springs finish filling buckets at the same time, so:

    [3x8+(8-X)]/2 = 8+X

    Then:

    X = 16/3,

    and the time taken is:

    t = 8 + 16/3 = 13 1/3 min.

    Which can be cross checked, as both springs are fully occupied
    during the filling process, so the total rate of filling is 3 ltrs/min
    and there are 40 ltrs to fill so time = 40/3 = 13 1/3 as required.

    Also all three people are required as we need two fillers and one
    mover simultaneously while the part filled bucket is moved from
    one spring to the other.

    RonL
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