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Joe can paint a garage in 24 hours, and Bobby can paint the same garage in 12 hours.  The two boys and their father can paint the garage in 4 hours.  How long would it take the father to paint the garage?

 May 15, 2020
 #1
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Joe's rate:      1 garage every 24 hours  =  1/24

Bobby's rate:  1 garage every 12 hours  =  1/12

Father's rate:  1 garage every 4 hours    =  1/4

 

time:  t

 

(rate)·(time)  +  (rate)·(time)  +  (rate)·(time)  =  1 job completed

                         (1/24)·t  +  (1/12)·t  + (1/4)·t  =  1

                                                      t + 2t + 6t  =  24                  (multiply by 24)

                                                                  9t  =  24

                                                                    t  =  24/9

                                                                    t  =  2 2/3 hrs  =  2 hrs 40 mins.

 May 15, 2020

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