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    drkhandwe's Avatar
    drkhandwe Posts: 1, Reputation: 1
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    #1

    Jul 29, 2009, 01:33 AM
    word based quadratic equation
    X require 5 days more to complete a work than Y. After starting a work for 4 days Y left the job and X completed the remaining work in 5 days. Please find out how many days they will reqiuer to complete the work individually.
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
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    #2

    Aug 20, 2009, 08:39 AM
    Let's call the time required for person X to complete the job and the time require for person Y to complete the job.

    Since we know that it requires person X and extra 5 days to complete it, we have:

    (1) .

    Now, let's also call the rate at which person X works and the rate at which person Y works.

    The time required for each person to finish the job is the reciprocal of their rate. (In other words, if a person can do of the job each day, it will take 3 days to complete the job).

    (2)
    (3)

    Finally, we know that the job required 4 days of work from Y followed by 5 additional days from X.

    (4) .

    The 1 on the right hand side of the equation represents 100% of the job completed. In other words, 4 days of work at Y's rate + 5 days of work at X's rate resulted in 100% of the job being finished.

    Now it's simply a matter of solving equations (1) and (4) simulataneously to find and , then plugging into (2) and (3) to find the times required for each individually.

    For what it's worth, I come up with

    or about 6.9 days, and
    or about 11.9 days.

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