If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the...
If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time?
Answer/Solution
a. 5
Steps/Work
You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 15 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 15*36 machine-days of work. So the job requires 15*36 days of machine work in total. We instead want the job done in 1/4 less time, so in 27 days. So we'll need 15*36/27 = 20 machines, or 5 additional machines.
A
We can solve this problem identically. If 15 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 15*36 machine-days of work. So the job requires 15*36 days of machine work in total. We instead want the job done in 1/4 less time, so in 27 days. So we'll need 15*36/27 = 20 machines, or 5 additional machines.
A