# 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?

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 $\frac{3}{40}$ of the work is completed

$\therefore$ to complete the job it takes$\frac{40}{3} = 13 \frac{1}{3} \min$

Nov 12, 2015

$t = 12 \text{ minutes " 20 " seconds}$

#### Explanation:

Consider rates per minute for each machine:

$A \to {\left(\frac{1}{30}\right)}^{t h}$ of the job

$B \to {\left(\frac{1}{40}\right)}^{t h}$of the job

$C \to {\left(\frac{1}{60}\right)}^{t h}$ of the job

These fractions are part of $\textcolor{b l u e}{1}$ complete job.

Let to total production time be t

$\textcolor{b l u e}{\text{Then (all production rates per minute)" times t_"minutes" =1 " job}}$

So:

$\frac{t}{30} + \frac{t}{40} + \frac{t}{60} = 1$

$\frac{4 t + 3 t + 2 t}{120} = 1$

$9 t = 120$

$t = \frac{120}{9} = 13 \frac{1}{3}$ minutes

$\textcolor{g r e e n}{t = 12 \text{ minutes " 20 " seconds}}$