If A can do it in 9 days and B in 8 days. How much days will C work it if they three can finish it in 3 days?

A,B and c can do a piece of work together in 3 days. A can do it alone in 9 days and B can do it alone in 8 days. How long will it take C to do the job alone? Can i have the answer and pls. tell me how you got it? Thanks a lot!

If A can do it in 9 days and B in 8 days. How much days will C work it if they three can finish it in 3 days?
Rate*Time=Work





A's rate is a piece of work per 9 days


B's rate is a piece of work per 8 days.





One piece of work=(a's rate*time)+(b's rate*time)+(c's rate*time)





1=(1/9)t+(1/8)t+Ct





We know the time because it says that it takes 3 days, so...





1=(1/9)(3)+(1/8)(3)+3C


1=(1/3)+(3/8)+3C


(7/24)=3C


C=7/72,





so C can perform 7 pieces of work in 72 days. That means that it will take C approximately 10.3 days to perform one piece of work.





I hope that this helped.
Reply:Take L.C.M of all the numbers . here L.C.M of 9,8,and 3 is 72.


say, there are 72 units of work to do.


A does 72/9 i.e 8 units of work each day.


B does 72/8 i.e 9 units of work each day.


Together, they can do 72/3 i.e 24 units of work each day.


that means 8+9+ amount of work by C=24


The amount of work done by C is=24-17=7 units of work each day


C will finish it in 72/7 days .
Reply:10 days if everyone can do it in 3 days, then the average person can do it in 9 days 3 x 3=9 3 people times 3 hours. Now if A can do it in 9 hours, then he is average. If B can do it in 8 hours he is only 1 hour less. so the answer is 10 cause its one hour more. 9 + 8 + 10 = 27 / 3 = 9 wich is the average.





c + 17 = 27, find c





JW
Reply:If we give the whole job a value of 1. Then A can do 1/9 in a day and B can do 1/8 in a day. Let's call c the amount C can do in a day. Then





3*(1/9+1/8+c)=1





since they can finish together in 3 days. Solving for c we find





1/3+3/8+3c=1


17/24+3c=1


3c=7/24


c=7/72





So C can do 7/72 of the work in a day. Thus it takes C 72/7, or about 10.3 days to do the work alone.
Reply:suppose each person works at a constant pace,





In 3 days,


A can do 3/9 (=1/3) of the work


B can do 3/8 of the work


the rest of the work is done by C





Therefore, C can do 7/24 of the work in 3 days...





For C to do 1/24 of the work, it would take 3/7 days.


Thus C takes (3/7 * 24) days to do the job alone.





The answer is 10 and 2/7 days or 72/7 days.