Final answer:
To find out how long the newer computer will take to send out an email on its own, we need to create an equation based on the given work rates of both computers. By setting up the equation and solving for x, where x represents the newer computer's time to complete the task alone, we determined it would take 18.75 minutes for the newer computer to send out the email by itself.
Step-by-step explanation:
The problem at hand is a classic work rate problem, asking us to determine how long it would take for the newer computer to send an email on its given that it takes four times less time than an older computer and that together they can complete the task in 15 minutes.
First, let's define the rate of work for each computer. We can assign the variable x to the time it takes the newer computer to send out the email on its own. Therefore, the older computer would take 4x time to do the same task on its own.
Next, we combine their work rates to find the total time they take working together. The work rate of the newer computer is 1/x of the job per minute, and the work rate of the older computer is 1/4x of the job per minute. Together, they can do (1/x) + (1/4x) = 1/15 of the job per minute since they finish it in 15 minutes.
Combining their rates, we get the equation 1/x + 1/4x = 1/15. Solving for x gives the time the newer computer takes to send the email on its own. 1/x + 1/4x = 1/15 converts to (4 + 1) / 4x = 1/15, which simplifies to 5/4x = 1/15.
Multiplying both sides by 4x to clear the fraction, we get 5 = 4x/15. Then, simplify and solve for x: x = (5 * 15) / 4 yields x = 18.75. Therefore, it takes the newer computer 18.75 minutes to send out the email on its own.