Question

X and Y can do a piece of work in 12 days. Y and Z can do it in 15 days while Z and X can finish it in 20 days. Din how days can X, Y, and Z finish it, they all work together? In how many days will each one of them finish it working alone?​

Answer 1

Step-by-step explanation:

Let’s define x, y and z as the portion of the total job that Messrs. X, Y and Z can do in a single day. Thus we have the system of equations:

x + y = 1/10

y + z = 1/12

x + z = 1/15

Subtracting the third equation from the first:

y - z = 1/30

y = z + 1/30

Substituting into second equation:

(z+1/30) + z = 1/12

2z + 1/30 = 1/12

2z = 5/60 - 2/60

2z = 1/20

z = 1/40

So Mr. Z needs 40 days to do the job by himself.

Substituting into the second equation:

y + (1/40) = 1/12

y = 1/12 - 1/40

y = 10/120 - 3/120

y = 7/120

So Mr. Y needs 120/7 = 17 17 days to do the job by himself.

Substituting into the third equation:

x + (1/40) = 1/15

x = 1/15 - 1/40

x = 8/120 - 3/120

x = 5/120 = 1/24

So Mr X. needs 24 days to do the job by himself.