Question

It takes an older computer twice as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 15 minutesto send out the email. How long will it take the newer computer to send out the email on its own?Do not do any rounding.

Answer 1

Firsly, let's work out an equation for the situation where both send e-mails in 15 minutes.

If x is how long it takes for the older computer to send one e-mail and y is how long it takes for the new computer to send the e-mail, then:

In 1 minute, the older comoputer can send 1/x fraction of the e-mail and the new computer 1/y fractio of the e-mail.

In 15 minutes, the older computer sent 15/x fraction of the e-mail and the new computer sent 15/y fractio of it. In total, they sent the whole e-mail, so, the sum of these fractions has to be 1:

`(15)/(x)+(15)/(y)=1`

Since the older computer take twice as long as the new computer, then x is equal to two times y:

`x=2y`

Substituteing this, we have:

`\begin{gathered} (15)/(2y)+(15)/(y)=1 \\ (15)/(2y)+(30)/(2y)=1 \\ (45)/(2y)=1 \\ 45=2y \\ y=(45)/(2) \\ y=22.5 \end{gathered}`

And now, for x, we have:

`\begin{gathered} x=2y \\ x=2\cdot22.5 \\ x=45 \end{gathered}`

Since y is the time for the new computer, it will take 22.5 minutes for the newer computer to send the e-mail on its own.