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Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How long would it take each of them to do the job​ alone?

 Mar 6, 2020
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Let          1/d    be the rate that Dwight works  [1 job every d hours]

Then 1/(d - 3)  is the rate that Joe works         [1 jobe every d - 3 hours] 

 

rate x time  =  amount done                      Total amount done is 1 job

 

(amount done by Dwight)  +  (amount done by Joe)  =  Total work done

        (1/d) x 2                     +       ( 1/(d - 3) } x 2         =  1

 

Mulriply both sides by  d · (d - 3):

 

    [d · (d - 3)] · (1/d) x 2   +  [d · (d - 3)] · ( 1/(d - 3) ) x 2  =  1 · [d · (d - 3)]

               2(d - 3)              +                2d                           =  d2 - 3d

                                                                      2d - 6 + 2d  =  d2 - 3d

                                                                                      0  =  d2 - 7d + 6

                                                                                      0  =  (d - 6)(d - 1)

If  d = 6 hours (Dwight), then  d - 3  =  3 hours (Joe).

 Mar 6, 2020

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