# Jake vs. Leo's car mileage

## Statement of Situation

Jake vs. Leo's car mileage over a year

## Situation

Two friends named Jake and Leo both get their license at the same time. So they both buy used cars with the money they both had been saving up for a car. Jake's car has a mileage of 46,000km when he buys his car and he travels 4,000km/month (rate). Leo's car has a mileage of 58,000km when he buys his car and he travels 2,000km/month (rate). They both track their mileage for a year. At the end of the year they compare their mileages with each other to see who travelled more. (shown in graph and table)

## Equations

Mileage (km) = d Month = m

Jake: d = 4000m + 46000

Leo: d = 2000m + 58000

## Explanation

The solution of this linear system shows the month when both Jake and Leo have the same mileage. The point of intersection shows that bot Jake's and Leo's car mileage is 7,000km at the 6th month. This point is when Jake catches up to Leo and both of them have the same mileage on their cars. After this point Jake continues to have more mileage than Leo because his rate is higher than Leo's. Before this point Leo started of with a higher mileage on his car than Jake.

## Summary Statement

Leo's mileage is more in the starting because when he bought the used car it had more mileage than Jake's. But Jake drove his car more than Leo, this resulted in Jake's mileage being more than Leo's mileage.