SOLUTION: 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 t

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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?
I was thinking along the lines of Average rate between them is 35 minutes and if both of them are mowing it will be half of that which is 17.5 minutes.
The answer in the back of the book states that it will take 120/7 minutes. I have no idea how they got these figures? Any assistance would be appreciated.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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
:
+ = 1
Multiply by LCM, 120 will work
120* + 120* = 120(1)
cancel the denominators and you have:
4t + 3t = 120
7t = 120
t =