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?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
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#
#t= 12" minutes " 20 " seconds"#
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")#
