# Thread: Time and Work hard problem

1. ## Time and Work hard problem

I am finding this really hard to do
A,B and C can complete a work in 12,15 an 20 days respectively.
• how long will it take to do the work together?
• If they start the work together,and C leaves for 2 days,then how long will it take for A and B to do the work together?

I did the first part and i got 5.

2. ## Re: Time and Work hard problem

When people (or machines, etc) work together, their rates add.
"A,B and C can complete a work in 12,15 an 20 days respectively."
So A's rate of work is "one job in 12 days" or 1/12 job per day. Similarly, B's rate is 1/15 job per day and C's is 1/20 job per day. Together they can do 1/12+ 1/15+ 1/20 job per day. 12= 4(3), 15= 5(3) and 20= 4(5) so the least common denominator is 3(4)(5)= 60. 1/12+ 1/15+ 1/20= 5/60+ 4/60+ 3/60= 12/60= 1/5 job per day. So you were right- at 1/5 job per day, they will complete the job in 5 days.

"If they start the work together,and C leaves for 2 days,then how long will it take for A and B to do the work together?"
So all three, A, B, and C, work for three days, at 1/5 job per day and so compete 3/5 of the job, leaving 2/5 of the job still to be done.
A and B working together, without C, have rate 1/12+ 1/15= 5/60+ 4/60= 9/60= 3/20 job per day.
At 3/20 job per day, how long will it take them to do 2/5 job?

3. ## Re: Time and Work hard problem

Thank You Sir
BTW it is 2/5 right? you wrote 2/4...........

4. ## Re: Time and Work hard problem

Yes, thanks, "2/4" was a typo.

5. ## Re: Time and Work hard problem

A similar method is to observe that lcm(12,15,20) = 60, so in 60 days: