Final answer:
By creating an equation for each person's annual mileage and solving for when they are equal, we find that Elena's and Marc's car mileages will not be the same at the end of a full year since the solution is not a whole number.
Step-by-step explanation:
To determine if Elena's and Marc's car mileages will ever be equal, we can set up an equation representing each person's yearly mileage. Let's define x as the number of years after the current year. Elena's mileage after x years will be 15,000 + 15,000x miles, and Marc's mileage after x years will be 24,000 + 11,000x miles.
Setting the equations equal to each other, we get:
15,000 + 15,000x = 24,000 + 11,000x
Subtracting 11,000x from both sides gives us:
4,000x = 9,000
Dividing both sides by 4,000 gives us:
x = 2.25
Since x represents whole years, and 2.25 is not a whole number, Elena's and Marc's car mileages will not be equal at the end of a full year. Therefore, their mileages will not exactly match at any given time because they cannot have driven a fraction of a year's worth of mileage.