A and B can do a piece of work in 20 days, B and C in 30 days, C and A in 40 days. Find:

a) How long will each woeker can do the work alone?
b) If the three work together,how long will they be able to finish the job?

Solution:
a) Let

A= rate of workman "A"
B= rate of workman "B"
C= rate of workman "C"

Condition 1:

A(20) + B(20) = 1 -----> equation 1

Condition 2:

B(30) + C(30) = 1 -----> equation 2

Condition 3:

A(40) + C(40) = 1 -----> equation 3

Solving the three equations simultaneously:

A= 5/240

B= 7/240

C= 1/240

therefore:

time for A is 48 days
time for B is 34.3 days
time for C is 240 days

note: on how we arrived on those answer is through using the equation t=1/rate of the worker which are worker A, worker B and worker C.

b) let t=time for A,B,C to finish the job by working together.

At + Bt + Ct = 1

(A + B + C)t = 1

t = 1/ ( A + B + C )

t = 1/ ( 5/240 + 7/240 + 1/240 )

t = 240/13 days