Machines A,B and C can complete a certain job in 30 min., 40 min. and 1 hour respectively. How long will the job take if the machines work together?

2 Answers
Nov 12, 2015

A-30 min
B - 40 min
C-60 min

Now this is in terms of time taken to do work;

So let the total work be x

Now in 1 min the work done is

#A->1/30 x; B -> 1/40 x; C->1/60 x#

So if we combine all 3 ie.

#1/30 x+ 1/40 x+1/60 x =3 /40 x#

Now in 1 min # 3/ 40# of the work is completed

#therefore# to complete the job it takes# 40/3= 13 1/3 min#

Nov 12, 2015

Answer:

#t= 12" minutes " 20 " seconds"#

Explanation:

Consider rates per minute for each machine:

#A -> (1/30)^(th) # of the job

#B -> (1/40)^(th )#of the job

#C -> (1/60)^(th) # of the job

These fractions are part of #color(blue)(1)# complete job.

Let to total production time be t

#color(blue)("Then (all production rates per minute)" times t_"minutes" =1 " job")#

So:

#t/30 + t/40 + t/60 =1#

#(4t+3t+2t)/(120) = 1#

#9t=120#

#t=120/9 =13 1/3# minutes

#color(green)(t= 12" minutes " 20 " seconds")#