9th algebra

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1.Jeff can weed the garden in 4 h. His wife takes the same amount of time. After they worked for 1 hr, their son helped them finish in 1/2 h. H long would it have taken Rory by himself to weed the garden?

  • 9th algebra -

    jeff's rate = 1/4
    wife's rate = 1/4
    combined rate = 1/4 + 1/4 = 1/2

    job done after 1 hr = (1/2)(1 hr) = 1/2

    let son's rate be 1/x , (who is Rory ? )

    combined rate = 1/4 + 1/4 + 1/x
    = 1/2 + 1/x
    = (x+1)/(2x)

    time for rest of job = (1/2)/combined rate)
    (1/2)/((x+1)/(2x))
    = (1/2)(2x/(x+1)
    = x/(x+1)

    but x/(x+1) = 1/2 hr
    2x = x+1
    x = 1

    So Rory could do the garden in 1 hour by himself

  • 9th algebra -

    eh?
    mom and pop each do 1/4 job in 1 hour
    so, 1/2 job remained when Rory came to work.

    In the next 1/2 hour, mom and pop each did another 1/8 of the job, or 1/4 combined.

    That left 1/4 of the job for Rory to do in 1/2 hour. So, Rory could do the whole job in 2 hours by himself.

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