Math word problems

Question

A new photocopier works twice as fast as an old one. When the machines work together, they can produce all its staff manuals in 15 hours. Find the time it will take each machine working alone, to complete the same job

Answer 1

Hello Jose,

Let's assign the variable t to the time it takes for the new photocopier to do the job alone.

The new photocopier works twice as fast. In other words, the old photocopier works twice as slow as the new one. So the time it takes for the old photocopier is 2 * t.

The old photocopier therefore works at a rate of 1/2t; meaning it does all the work in 2t hours

The new photocopier works at a rate of 1/t; meaning it completes the work in t hours.

The machines working together means you add the rates, NOT the hours so:

(1/2t) + (1/t) = (together rate) = 1/15 [Remember the problem says the machines complete the work together in 15 hours]

Bringing (1/2t) and (1/t) to a common denominator, you get: (1/2t) + (2/2t) = 1/15 so 3/2t=1/15

Cross-multiplication gives you the following equation: 2t=45 so t = 22.5 hours

So the new photocopier will complete the job alone in 22.5 hours, while the old photocopier will complete the job alone in 45 hours (2 times 22.5 = 45).

Cheers!