the copy center can do the printing job in 7 hours using copier A.Copier B can do the job in 12 hours.how long will it take if both copiers work at the same tim

Question

Please help.how long will it take if the copiers work at the same time?

Answer 1

Hanna,

 

Copier A doing the whole job in seven hours is the same a doing 1/7th of the job per hour, likewise B does 1/12th of the job in an hour. Together they do 1/7th + 1/12th of the job per hour.

 

To add the fractions you need to change them so they have the same denominator. This would be 12/84 + 7/84 doing cross multiplication and would add up to 19/84. So the combined rate of work would be 19/84ths of the job every hour.

 

To get back to the number of hours you would find x so that x(19/84) = 1, or 19/84 = 1/x, or 19x = 84, or x = 84/19, or x = 4 8/19. In other words a little over four hours and 24 minutes. You could get closer by continuing to factor 8/19 into minutes and seconds.