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 25 minutes to send out the email. How long will it take the newer computer to send out the email on it's own?

Answer 1

Answer:

It will take 37.5 minutes for the newer computer to send an email on its own.

Step-by-step explanation:

Given:

Number of minutes taken by 2 computers to send an email = 25 mins

We need to find the Number of minutes taken by newer computers to send an email.

Solution:

Let the Number of minutes taken by newer computer to send an email be $'x'$.

Now Given:

It takes an older computer twice as long to send out a company's email as it does a newer computer.

So we can say that;

Number of minutes taken by older computer to send an email = $2x$

Now we can say that;

Rate is given by 1 job completed divided by Time required to complete the job.

Rate of newer computer = $\frac{1}{x}$

Rate of older computer = $\frac{1}{2x}$

Rate when both work together = $\frac{1}{25}$

Now we can say that;

Rate when both work together is equal to sum of Rate of newer computer and Rate of older computer.

framing in equation form we get;

$\frac{1}{x}+\frac{1}{2x}=\frac{1}{25}$

Now we will make denominator common using LCM we get;

$\frac{1\times2}{x\times2}+\frac{1\times1}{2x\times1}=\frac{1}{25}\\\\\frac{2}{2x}+\frac{1}{2x}=\frac{1}{25}$

Now we will solve the numerator as denominator are common.

$\frac{2+1}{2x}=\frac{1}{25}\\\\\frac{3}{2x}=\frac{1}{25}$

By Cross multiplication we get;

$3\times25 =2x\\\\75= 2x$

Dividing both side by 2 we get;

$\frac{75}{2}=x\\\\x=37.5 \ mins$

So we can say that;

Number of minutes taken by newer computer to send an email = 37.5 mins

Number of minutes taken by older computer to send an email = $2x = 2\times37.5 = 75\ mins$

Hence It will take 37.5 minutes for the newer computer to send an email on its own.