SOLUTION: Arpit can fence a garden in 3 hours, Ankur can do it in 5 hours and Aakash takes 6 hours to do the same. If they work together, in how many hours they can fence the garden?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Arpit can fence a garden in 3 hours, Ankur can do it in 5 hours and Aakash takes 6 hours to do the same. If they work together, in how many hours they can fence the garden?      Log On


   

Question 828248: Arpit can fence a garden in 3 hours, Ankur can do it in 5 hours and Aakash takes 6 hours to do the same. If they work together, in how many hours they can fence the garden?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes to fence the garden if they work together
So, together, they work at the rate of 1/x of the garden per hour
Arpit works at the rate of 1/3 of the garden per hour
Ankur works at the rate of 1/5 of the garden per hour
Aakash works at the rate of 1/6 of the garden per hour
So, our equation to solve is:
1/3 + 1/5 + 1/6 = 1/x multiply each term by 30x
10x+6x+5x=30
21x=30
x=1 3/7 hours
CK
In 1 3/7= 10/7 hours, Arpit can fence (1/3)(10/7)=10/21 of the garden
In 10/7 hours, Ankur can fence (1/5)(10/7)=2/7 of the garden
In 10/7 hours, Aakash can fence (1/6)(10/7)=10/42 of the garden
Sooooo, 10/21 + 2/7 + 10/42 should equal 1 (garden, that is)
20/42 +12/42 + 10/42=42/42=1
Hope this helps---ptaylor