together, 15 type a machines and 7 type b machines can complete a certain job in 4 hours. together 8 type b machines and 15 type c machines can complete the same job in 11 hours. how many hours e would it take one type a machine, one type b machine, and one type c machine working together to complete the job ( assuming constant rates for each machine )?
Choose the correct choice from the following answers:
A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) it can not be determined from the information above .
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>

<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>

<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>

<result>C</result>
together, 15 type a machines and 7 type b machines can complete a certain job in 4 hours. together 8 type b machines and 15 type c machines can complete the same job in 11 hours. how many hours e would it take one type a machine, one type b machine, and one type c machine working together to complete the job ( assuming constant rates for each machine )?
divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))
say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .