Question 578103
Tom and Jerry have a mowing business. 
It takes Tom 30 minutes to mow a yard and it takes Jerry 40 minutes to mow the same yard.
 If they work together, how long will it takes them to mow the yard?
:
This is a shared work problem, and here is a simple method:
:
let t = time required when working together (assume they have two mowers)
let the completed job = 1 (a mowed yard)
:
Each boy will do a fraction of the lawn, the two fractions must add up to 1
:
{{{t/30}}} + {{{t/40}}} = 1 
Multiply by LCM, 120 will work
120*{{{t/30}}} + 120*{{{t/40}}} = 120(1)
cancel the denominators and you have:
4t + 3t = 120
7t = 120
t = {{{120/7}}}