Question

Elena and her husband Marc both drive to work. Elena's car has a current mileage (total distance driven) of 15,000 and she drives 15,000 miles more each year. Marc's car has a current mileage of 24,000 and he drives 11,000 miles more each year. Will the mileages for the two cars ever be equal? Explain

Answer 1

Let us set up a system of functions to describe the given situation and see if they ever intersect.

Elena has initially 15000 miles and adds 15000 per year.

we can describe it as Elena = 15000+15000(years).

Marc's equation can be given as = 24000+11000(years).

Setting both conditions equal, we get

15000+15000(years)=24000+11000(years).

Clubbing years on one side we get,

4000(years)=9000

Lets divide by 4000 on each side we get years = 2.25

Hence yes, the mileages will equal the same value (whatever it may be) in 2.25 years from the the beginning of the problem.