Question

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
a) 6
b) 9
c) 12
d) 27
e) 48

Answer 1

Answer:

b) 9

Step-by-step explanation:

Given: Three machines  operating independently, simultaneously, and at the same constant rate can fill a certain production order in $36$ hours.

To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.

Solution:

Let  the time taken by one machine to fill a certain production alone be$=\text{x}$

Time taken when three machine operate independently and simultaneously

$\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}$

$\frac{3}{\text{x}}=\frac{1}{36}$

$\text{x}=108$ $\text{hours}$

Let time taken when one additional machine is used $=\text{y}$

Time when when one additional machine is used

$\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}$

$\frac{4}{108}=\frac{1}{\text{y}}$

$\text{y}=27$ $\text{hours}$

it takes $27$ $\text{hours}$ when one additional machine is used

Now,

fewer hours taken when one additional  machine is used

$=\text{number of hours taken when three machines are used}-$$\text{number of hours taken when one additional machine is used}$

$36-27$

$9$ $\text{hours}$

in $9$ fewer hours of simultaneous operation the production order can be filled if one additional machine is used

Hence option b) is correct.