Question 469791
Since Sally can paint a house in 4 hours, in an hour she completes 1/4 of the house.  And since John can paint the same house in 6 hours, in an hour he completes 1/6 of the house.  Therefore, in one hour the sum of their combined efforts is:
.
{{{1/4 + 1/6}}}
.
of the job.
.
Add these two fractions by converting them to the common denominator of 12 to get:
.
{{{3/12 + 2/12 = 5/12}}}
.
So in each hour they complete five twelfths of the one job.
.
The question, therefore, is how many hours (call them t for time) does it take for them to complete the entire one job (that is 12 twelfths of the job). Set up the following equation:
.
{{{(5/12)*t = 12/12}}}
.
Solve this equation by first multiplying both sides of the equation by 12 to eliminate the denominator of 12 and get:
.
{{{5t = 12)}}}
.
Solve this equation by dividing both sides by 5:
.
{{{t = 12/5}}}
.
and divide 12 by 5 to get the answer:
.
{{{t = 2.4}}}
.
So it takes 2.4 hours for them working together to paint the house. (And since there are 60 minutes in an hour, the 0.4 of an hour is {{{60*0.4 = 24}}} minutes.) Therefore, working together they will complete the job in 2 hours and 24 minutes.
.
Hope this helps you to understand the problem better.
.