For this case, the first thing we must do is define a variable.
We have then:
x: amount of time it takes for the newest machine to complete the work by working alone.
We know that the new machine is twice as fast as the old machine.
As both machines work together and the time is 14 hours the equation is given by:
[tex] \frac{1}{x} +\frac{1}{2x} =\frac{1}{14} [/tex]
Rewriting the equation we have:
[tex] \frac{14x}{x} +\frac{14x}{2x} =\frac{14x}{14} [/tex]
[tex]x=14+7
x=21 [/tex]
Then, the time it takes for the oldest machine to complete the work is given by:
[tex] 2x=2*21
2x=42 [/tex]
Answer:
New machine: 21 hours
Old machine: 42 hours
