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math

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1.A father can do a job in a certain number of hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does it take the father to do the job alone?
A.9
B.18
C.12
D.10

3.David is 5 years older than Paul. In 5 years, David will be twice as old as Paul is now. How old is David now?
A.15
B.10
C.25
D.20
this is what i have so far:
D=p+5
2D+p(i'm not sure if this is right)

  • math - ,

    1.

    combined rate=1/F +.5/F=1.5/F=1/6

    f=9 hrs

    D-5=P
    D+5=2P
    subtract second equation from first
    -10=-P P is 10 now, so D is 15

  • math - ,

    job/rate = time --> rate = job/time

    let the fathers rate = job/x
    let the son's rate be job/2x

    combined rate =job/x + job/2x
    = 3job/(2x)

    combined time = job รท(3job/2x)
    = job (2x/3job)
    = 2x/3

    but 2x/3 = 6
    2x = 18
    x = 9

    It would take 9 hrs for the father to work alone

    3.
    Paul's age --- x
    David's age -- x+5

    in 5 years:

    David --> x+10

    x+10 = 2x
    x = 10

    Paul is now 10 and David is now 15

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