how long would jeff need to do the job alone

Question

matt and jeff need to paint a fence. matt can do the job alone in 12 hours. if together they work for 5 hours and only finish 7/8 of the job, how long would jeff need to do the job alone

Answer 1

In 5 hours Matt will finish 5/12 of the job and Jeff will finish 5/J of the job where J is the number of hours J would require to do it alone.  Together they finish 7/8 of the job in 5 hours, i.e. (in math terms):

 

(5/12) + (5/J) = 7/8

5/J= (7/8) - (5/12) = 11/24

5/J = 11/24 => J/5 = 24/11 => J = 120/11 = 10 10/11 hours for Jeff to do the whole job by himself.

 

You should that this answer satisfies the specifications in the original problem.