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.

Option B - 9 hours

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. If one additional machine were used under the same operating conditions.

To find : In how many fewer hours of simultaneous operation could the production order be filled?

Solution :

Let the numbers of hours taken including additional machine i.e. 4 machines be 'x' hours.

So, 3 machines take 36 hours

and 4 machines take x hours.

Then,

i.e. 4 machines spend 27 hours to do work.

Number of fewer hours of simultaneous operation could the production order be filled is given by,

hours

Therefore, the work could be done in 9 hours less.

So, the correct answer is B.

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value