SOLUTION: An old machine requires 3 times as many hours to complete a job as a new machine. When both machine work together, they require 9 hours to complete a job. How many hours would it t

Question 1087139: An old machine requires 3 times as many hours to complete a job as a new machine. When both machine work together, they require 9 hours to complete a job. How many hours would it take then new machine to finish job alone?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity of work

quantity of work = 1 job.

formula becomes rate * time = 1

let T = time and R = rate and the formula becomes:

R * T = 1

the old machine takes 3 times as long to finish the job as a new machine.

formula for old machine becomes R * 3T = 1

formula for new machine becomes R * T = 1

solve for R in both equations.

R = 1/(3T) for the old machine.

R = 1/T for the new machine.

when they work together, their rates are additive.

therefore (1/(3T) + 1/T) * 9 = 1

convert to common denominators to get:

(1/(3T) + 3/(3T) * 9 = 1

combine like terms to get:

4/(3T) * 9 = 1

simplify to get 36/(3T) = 1

simplify further to get 12/T = 1

solve for T to get T = 12

the formula for the old machine is R * 3T = 1

therefore, the old machine takes 36 hours to finish the job alone.

the formula for the new machine is R * T = 1

therefore, the new machine takes 12 hours to finish the job alone.

your solution is that the new machine takes 12 hours to finish the job alone.

the rate of the old machine is derived from R * 36 = 1 to get R = 1/36.

the rate of the new machine is derived from R * 12 = 1 to get R = 1/12

you can confirm the solution is correct by using the formula (R1 + R2) * T = 1 for when they work together.

R1 = 1/36
R2 = 1/12

formula becomes (1/36 + 1/12) * T = 1

combine fractions together to get 4/36 * T = 1

solve for T to get T = 36/4 = 9.

this is what was given when they work together so the solution is confirmed as good.

the solution is, once again, 12 hours to complete the job when the new machine is working alone.

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

An old machine requires 3 times as many hours to complete a job as a new machine. When both machine work together, they require 9 hours to complete a job. How many hours would it take then new machine to finish job alone?

Let time new machine takes be N
Then old machine can do work in 3N hours
Also, new and old machines can do and of work, in 1 hour, respectively
We then get:
9 + 3 = N ------ Multiplying by LCD, 9N
N, or time new machine takes =
That's all! It's as SIMPLE as that!
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