Question

it takes an older computer 4 times as long to send out a company's email as it does in newer computer working together it takes the two computers 5 minutes to send out an email how long will it take the newer computer to send out the email on its own ?

Answer 1

We have a problem where we have to relate the capacities of an old and a new computer.

We will call C1 the capacity of the old computer and C2 the capacity of the new computer.

We define the capacity as the inverse of the time it takes to complete the task T:

$\begin{gathered} C_1=\frac{T}{t_1_{}} \\ C_2=\frac{T}{t_2} \end{gathered}$

That means that the less time it takes to complete the task, the higher the capacity is.

We know that the capacity of the new computer is 4 times the capacity of the old computer:

$C_2=4\cdot C_1$

If the computers work together they add their capacity, so we have:

$C_1+C_2=\frac{T}{t_3}$

We know that the time it takes for the two computers is 5 minutes, so we can write:

$\begin{gathered} C_1+C_2=\frac{T}{t_3}=\frac{T}{5} \\ \frac{C_2}{4}+C_2=\frac{T}{5}_{}_{} \\ \frac{5}{4}C_2=\frac{T}{5} \\ C_2=\frac{T}{5}\cdot\frac{4}{5} \\ C_2=\frac{T}{\frac{25}{4}}=\frac{T}{t_2} \\ t_2=\frac{25}{4}=6.25 \end{gathered}$

We then know that the time it takes for the new computer to complete the task on its ownis 6.25 minutes.

Answer: 6.25 minutes.