how long will it take the faster computer to do the job on its own?

Question

Working together, it takes two computers
12
minutes to send out a company's email. If it takes the slower computer
30
minutes to do the job on its own, how long will it take the faster computer to do the job on its own?

Answer 1

Let's think about this. The slower machine takes 30 minutes on its own. When the computing power is combined with a faster computer, it takes them only 12 minutes.

 

Let x represent the speed of the slower computer and y represent the speed of the faster computer. The work the slower computer does (30 minutes of work times x units of work per minute) is the same as the combined rates of both computers working for only 12 minutes.

 

30 * x = 12 * (x + y) = 12x + 12y

18x = 12y

 

Dividing both sides by 12, we get

 

1.5x = y

 

What does that mean? The faster computer has a speed y, which is 1.5 faster than x. So y is 1.5 times greater than x. If it takes a computer with speed x, 30 minutes to do the job, it will take a computer with speed y only (30 ÷ 1.5) minutes. The faster computer will need 20 minutes on its own.