John does a work in 6 hours. Silvester does the same work in 4 hours. If they both work together?

In how many hours will they complete the work...........plzzzz show working.........thank u very much

5 Answers

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  • John
    Lv 7
    1 decade ago
    Favorite Answer

    If John does it in 6 hours, he can complete 1/6 of the job in one hour. Silvester can do 1/4 of the job in an hour.

    How long it will take them is their combined work effort = 1/6 + 1/4 = times the time it takes them. And they'll complete ONE whole job.

    t*(1/4 + 1/6) = 1. 1/4 + 1/6 = 5/12.

    t(5/12) = 1.

    t = 12/5 = 2.4 hours or 148 minutes.

  • 1 decade ago

    John = 1/6 jobs/hr

    Silvester = 1/4 jobs/hr

    John and Silvester = 1/6 + 1/4 = 5/12 jobs/hr

    Time = 12/5 or 2.4 hrs/job

  • JG
    Lv 5
    1 decade ago

    John's rate is 1/6 of the task per hour

    Silvester's is 1/4 of the task per hour

    Together they do 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the task per hour.

    So it will take 12/5 hours which is 2.4 hours or 2 hours, 24 minutes.

  • 1 decade ago

    First quantify the word problem.

    Rate of work x time = work

    RT=W

    Find the rate of work for John:

    R* 6 hr = 1

    R = 1/6

    Rate of work for SIlvester.

    R*4hr = 1

    R= 1/4

    Now with both their rates of work, which will remain the same, and the amount of work, which will remain the same, solve for time.

    R1T+R2T=W

    1/6T+1/4T=1

    2/12T+3/12T=1

    5/12T=1

    12/5 hr = T

    2 2/5 hr = 2 hours 24 minutes

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  • Como
    Lv 7
    1 decade ago

    Let work to be done = X units

    ___________________John______Silvester

    rate of work (units/h)___X/6________X/4

    Working together , the work done per hour is:-

    X/6 + X/4 = 2X/12 + 3X/12 = 5X/12

    Time = Work done / rate of work

    Time = X / 5X/12 h

    Time = 12/5 h = 2 2/5 h = 2h 24 min

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