Question

A and B can do a piece of work in 28 days, B and C do it in 24 days, while C and A can finish it in 36 days. If A,B,C work together, in how many days will they finish the work?
Step by step​

Answer 1

Answer:

A finishes work W in 24 days

B finishes work W in 16 days

C finishes work W in x days

Together they complete work in 8 days.

What is the rate of work that A, B & C can complete?

A’s rate is W/24 days (Work per day)

B’s rate is W/16 days

C’s rate is W/x days

When A, B & C work together, their rates get added (unless they get in each other’s way!), since there are more people doing more work per day than before.

Therefore the number of days taken to complete work W when A, B & C work together is W/(A’s rate + B’s rate + C’s rate)

We know the number of days taken for them to complete wor together is 8 days.

Therefore:

8 = W/(W/24 + W/16 + W/x) , or

8 = W/(W *16*24 + W*24*x + W*16*x)/24*16*x

or 8 = 384*x/(384 + 40*x)

or 384*8 + 40*8*x = 384*x

or 3072 = 64*x

or x = 48 days

Therefore C would take 48 days to complete the work alone.

Answer 2

Step-by-step explanation:

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