SOLUTION: It takes you 30 mins to rake the leaves in your yard. It takes your brother 45 mins to rake your yard. How long would it take if you both worked together? Would the answer be 1

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes you 30 mins to rake the leaves in your yard. It takes your brother 45 mins to rake your yard. How long would it take if you both worked together? Would the answer be 1      Log On


   



Question 895277: It takes you 30 mins to rake the leaves in your yard. It takes your brother 45 mins to rake your yard. How long would it take if you both worked together?
Would the answer be 15 i'm so confused

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes you 30 mins to rake the leaves in your yard.
It takes your brother 45 mins to rake your yard.
How long would it take if you both worked together?
:
Here is an easy method to do "shared-work" problems:
let t = time required when working together
let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
t%2F30 + t%2F45 = 1
multiply by the least common multiple of 30 and 45, that would be 90
90*t%2F30 + 90*t%2F45 = 90(1)
cancel the denominators
3t + 2t = 90
5t = 90
t = 90/5
t = 18 minutes working together
:
:
You can check this for yourself, find what fraction of the job each does
18%2F30 + 18%2F45 =
reduce the fraction to a common denominator of 15
9%2F15 + 6%2F15 = 15%2F15 = 1