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Homework Help: Increasing the number of workers reduces the number of days

  1. Nov 30, 2016 #1
    1. The problem statement, all variables and given/known data
    If 15 workers can pave 18 driveways in 24 days, how many days would it take 40 workers to pave 22 driveways?

    2. Relevant equations

    Set of worker * driveways* days/Another set of workers * driveways
    3. The attempt at a solution
    15 * 18 *24/40 * 22 =54/11 wrong

    Some body plz guide. I don't know the method for solving such problems. I don't know the usage of two set of data.
  2. jcsd
  3. Nov 30, 2016 #2

    Doc Al

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    Staff: Mentor

    The "trick" is that the number of driveways per day per worker is a constant:

    (#driveways)/[(#workers)*(#days)] = constant

    So set up an equation comparing that expression (on the left) for the first set of data (15 workers, etc.) to one for the second set of data (40 workers, etc.). The only unknown will be the #days in the second set. Solve!
  4. Nov 30, 2016 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Do not just write down numbers without thinking. You need to approach such problems systematically.

    For example, how long would it take 1 worker to pave 18 driveways? From that, how long would it take 1 worker to pave 1 driveway? Now continue from that.
  5. Dec 1, 2016 #4
    Did you mean:
    15/(18 * 24) = 40/(20 * Days)

    Still the answer is not correct.
    I know that: if we increase the labors less days would be required to construct a drive way. So from 15 workers to 40 workers 2 days reqd for a driveway.
    15*24/40 = 9 days required for a drive way.

  6. Dec 1, 2016 #5

    Doc Al

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    Staff: Mentor

    The left hand side makes sense. How did you get the right hand side?

    Both sides must have this form:
  7. Dec 1, 2016 #6
    Thanks. I got the answer.
    First part (LHS): # of driveways = 18
    #of workers = 15
    # of days =24
    Second part(RHS):
    #of drive ways = 22
    #of days = ?
    #of workers=40
    (#driveways)/[(#workers)*(#days)] of First part= (#driveways)/[(#workers)*(#days)] of Second part
    Putting values:
    18/(15 * 24) = 22/(40* days)
    days = 11


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