a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
"yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 12 lets say x machines are used to attain the desired rate , thus x / 36 + x / 12 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 3 x ) / 36 = 1 / 2 4 x / 36 = 1 / 2 x = 9 / 2 . qa = 9 / 2 ( answer d )"
divide(const_1, multiply(12, add(divide(const_1, 36), divide(const_1, const_2.0))))