Math World Problem (functions)?

If Sue and Bill work together on a job, they can do the job in 7 hours. If Bill works alone, it takes him 15 hours. Write an equation to find out how long the job would take Sue working alone.

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  • sepia
    Lv 7
    4 weeks ago

    If Sue and Bill work together on a job, they can do the job in 7 hours.

    If Bill works alone, it takes him 15 hours.

    1/15 + 1/x = 1/7

    1/x = 8/105

    8x = 105

    The job would take Sue 13 1/8 hours working alone.

  • 4 weeks ago

    Unit of work per hour by Bill = W/15, where w is total units (the work).

    Unit of work by both = W/7,

    Unit of work by Sue = W/r, where h given no. of hours alone by Sue.

    But, W/7 - W/r = W/15,

    1/7 - 1/15 = 1/r,

    r = 15*7/8 hours = 105/8 = 13 hour 07 min 30 s.

  • Como
    Lv 7
    4 weeks ago

    -

    Let work to be done be A units

    Combined rate = A/7 units/hour

    rate for Bill = A/15 units/hour

    rate for Sue = A/t units/hour

    1/7 = 1/15 + 1/t

    1/7 - 1/15 = 1/t

    15/105 - 7/105 = 1/t

    8/105 = 1/t

    t = 105/8 = 13 h 7½ min______time for Sue working alone

  • 4 weeks ago

    If Sue and Bill work together on a job, they can do the job in 7 hours.

    If Bill works alone, it takes him 15 hours.

    1/7 - 1/15 = 1/s

    15s - 7s = 105

    8s = 105 h

    s = 13 1/8 h

    It would take Sue 13 h 7 m 30 s to do the job working alone.

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  • Vaman
    Lv 7
    4 weeks ago

    a is the rate of work for Sue. b is the rate of work for bill, Work is 1

    If they work together, the time is

    1/(a+b)=7, 1/b=15. 1= 7(a+b), 1=15b, You have

    15 b =7a+7b. 8b=7a, a=8/7 a = 8/105. Sue's working rate is 8/105

    Check it.

    a+b=1/15+8/105=15/105=1/7

    1/7 work per day. 7 days to complete. For Sue along it will take 105/8 days. 13 +1/8 days.

  • 4 weeks ago

    simple formula for when both work alone are known

    Sue*Bill / Sue+Bill

    for when just one work alone is known (simple algebra)

    Sue alone = Bill*both / Bill-both

    15*7 / 15-7 = 105/8 (about 13 1/8 hours)

    try it. you will like it

  • ted s
    Lv 7
    4 weeks ago

    ....unit rates for Sue + Bill = 1 / 7 , while for Bill it is 1 / 15 ===> unit rate for Sue is ( 1 / 7 ) - ( 1 / 15) = 8 / 105 ===> Sue takes 105 / 8 = 13 1/8 hours

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