### Author Topic: Time and Work Problem  (Read 4104 times)

#### samuel dhas

• Newbie
• Posts: 1
##### Time and Work Problem
« on: March 21, 2014, 10:18:18 PM »
Hello from Samuel.....   I need answer to this question...

A and B can do a work in 12 days, while B and C can do the work in 6 2/3 days. After A had worked on it for 3 days and B for 4 days, C finished the work in 7 days.
In how may days can A alone complete the work?

#### Shachi

• Newbie
• Posts: 2
##### Re: Time and Work Problem
« Reply #1 on: June 24, 2014, 05:07:34 AM »
if A and B works together then they complete the work in 12 days

1/A+1/B=1/12------>(eqn 1)

if B and C works together then they complete the work in 20/3 days

1/B+1/C=3/20------>(eqn 2)
Now,
A works for 3 days and B works for 4 days and C works for 7 days so the equation for this

3/A+4/B+7/C=1

Substitute the value of 1/A and 1/C  from equation 1 and 2 then we get,
3(1/12-1/B)+4/B+7(3/20-1/B)=1
1/B=1/20
now put 1/B=1/20 in equation 1 so we get,
1/A=1/30
that means A alone can complete the work in 30 days.