SOLUTION: a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working      Log On


   

Question 125606: a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans?
:
Let x = time for the new machine to do the job by itself
then
3x = time required for the old machine to do the job by itself, (take 3 times as long)
:
Let the completed job = 1; (the making of 10,000 cans)
:
9%2F%283x%29 + 9%2Fx = 1
:
Multiply equation to get rid of the denominators and you have:
9 + 3(9) = 3x
:
9 + 27 = 3x
:
36 = 3x
x = 36%2F3
x = 12 hrs, new machine working by itself
:
Check solution in original equation (old machine time 3*12 = 36hrs)
9%2F36 + 9%2F12 = 1
1%2F4 + 3%2F4 = 1