Work Problem No. 1

Dan can do the job in 30 hours, Ellen can do it in 40 hours, and Francis can do it in 60 hours. how long would it take them if they work together?

Solution:

Let x be the number of hour Dan, Ellen, and Francis take if they work together.

Name                Rate (job per hour)         Time                  Work
Dan                             1/30                       x                         x/30
Ellen                            1/40                       x                         x/40
Francis                        1/60                       x                         x/60

Equation:              x/30  + x/40  +  x/60  =  1

To solve, multiply both sides of the equation by the LCD, i.e.

120 (  x/30  + x/40  +  x/60 ) = ( 1 ) 120
                      4x  + 3x  + 2x  =  120
                                        9x  =  120
                                          x  =  120/9
                                          x  =  13 1/3 hours or 13 hours and 20 minutes.

Therefore, Dan, Ellen, and Francis can finish the job in 13 hours and 20 minutes if they work together.


Problem is taken from e-math kto12 grade 7