Question

A new photocopier works 2 times as fast as an old one. when the machines work​ together, a university can produce all its staff manuals in 14 hr. find the time it would take each​ machine, working​ alone, to complete the job.

Answer 1

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:

$\frac{1}{x} +\frac{1}{2x} =\frac{1}{14}$

Rewriting the equation we have:

$\frac{14x}{x} +\frac{14x}{2x} =\frac{14x}{14}$

$x=14+7 x=21$

Then, the time it takes for the oldest machine to complete the work is given by:

$2x=2*21\\2x=42$

Answer:

New machine: 21 hours

Old machine: 42 hours