if 16 machine can finish a job in 45 days , then how many more machines would be needed to finish the job in one - third less time ?
"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 16 machines ( identical ones , i assume ) work simultaneously for 45 days , they will do a total of 16 * 45 machine - days of work . so the job requires 16 * 45 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 30 days . so we ' ll need 16 * 36 / 30 = 19.2 ~ = 19 machines , or 3 additional machines . a"
subtract(divide(multiply(16, 45), multiply(divide(const_3, const_4), 45)), 16)