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 23,000 miles more each year. Marc's car has a current mileage of 46,000 and he drives 9,000 miles more each year. Will the mileages for the two cars ever be equal? Explain.

Answer 1

Answer: Yes, It will be equal in 2.2 years

Explanation:

Hi, to answer this question we have to write an equation for the mileage of Elena and Marc.

Elena = 15,000+ 23,000x

Marc= 46,000+ 9,000x

Wheres x is the number of years

So, if both have the same mileage

15,000+ 23,000x = 46,000+ 9,000x

Solving for x

23,000x-9,000x =46,000-15,000

14,000x = 31,000

x = 31,000/14,000

x = 2.21 years

Answer 2

In 2.2 years they will be equal the same value.

Explanation:

Let x = Number of years;

Elena = 23000x + 15000

Marc = 9000x + 46000

Then if we set Marc equal to Elena:

23000x + 15000 = 9000x + 46000

or

23000x - 9000x = 46000 - 15000

14000x = 31000

x = 31000 / 14000

x = 2.2

=> In 2.2 years they will be equal the same value.

=> In 2 years 2 months and 17 days Marc and Elena Cars' mileage will be equal.