Question

Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

• A. 3
• B. 5
• C. 6
• D. 8

Answer 1

The Correct Option is C

The work done by four machines in 30 hours is the same as the total work done. The rate of work for four machines is \( \frac{1}{30} \) of the total work per hour. The rate of work for one machine is: \[ \frac{1}{30} \times \frac{1}{4} = \frac{1}{120} \, (per hour) \] The rate of work for five machines working together is: \[ 5 \times \frac{1}{120} = \frac{5}{120} = \frac{1}{24} \, (per hour) \] The number of hours for five machines to complete the work is the reciprocal of \( \frac{1}{24} \), which is 24 hours. 
The time difference is: \[ 30 - 24 = 6 \, hours \] To calculate time saved when more machines work together, find the combined rate of work and subtract the time it takes for more machines from the time it takes for fewer machines.