SOLUTION: During one week, two machines produce a total of 27 210 parts, with the faster machine working for 37.5 h and the slower for 28.2 h. During another week, they produce 59 830 parts,

Algebra ->  Rate-of-work-word-problems -> SOLUTION: During one week, two machines produce a total of 27 210 parts, with the faster machine working for 37.5 h and the slower for 28.2 h. During another week, they produce 59 830 parts,      Log On


   

Question 1146597: During one week, two machines produce a total of 27 210 parts, with the faster machine working for 37.5 h and the slower for 28.2 h. During another week, they produce 59 830 parts, with the faster machine working 66.5 h and the slower machine working 88.6 h. How many parts can each, working
alone, produce in an hour?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the slow machine
y, the fast machine
those rates in PARTS per HOUR

system%2828.2x%2B37.5y=27210%2C88.6x%2B66.5y=59830%29
Simplify and solve the system.

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A possible way but not the only way to start solving the system:
From first equation
37.5y=27210-28.2x
y=%2827210-28.2x%29%2F37.5

subst. to second equation
88.6x%2B66.5%28%2827210-28.2x%29%2F37.5%29=59830
88.6x%2B66.5%2827210%2F37.5-28.2x%2F37.5%29=59830
88.6x%2B66.5%2A27210%2F37.5-66.5%2A28.2x%2F37.5=59830
88.6x-66.5%2A28.2x%2F37.5=59830-66.5%2A27210%2F37.5
%2888.6-66.5%2A28.2%2F37.5%29x=59830-66.5%2A27210%2F37.5
x=%2859830-66.5%2A27210%2F37.5%29%2F%2888.6-66.5%2A28.2%2F37.5%29
x=300
and you should be able to figure the rest and to finish.