Sure! Let's work through this step-by-step to complete the problem based on the given details.
### Step 1: Calculate the minimum distance driven per week.
You live 17 miles from work. This means you travel 17 miles to work and 17 miles back home each day. Thus, the total distance traveled in a day is:
- [tex]\( 17 \, \text{miles (to work)} + 17 \, \text{miles (back home)} = 34 \, \text{miles/day} \)[/tex]
Since you work 5 days a week, the total distance traveled in a week is:
- [tex]\( 34 \, \text{miles/day} \times 5 \, \text{days/week} = 170 \, \text{miles/week} \)[/tex]
So, you can expect to drive a minimum of 170 miles per week.
### Step 2: Calculate the minimum distance driven per year (excluding vacation).
You will work about 48 weeks per year. Therefore, the total distance driven for work in a year is:
- [tex]\( 170 \, \text{miles/week} \times 48 \, \text{weeks/year} = 8,160 \, \text{miles/year} \)[/tex]
Thus, you can expect to drive a minimum of 8,160 miles per year for work.
### Step 3: Include the vacation miles.
You have a planned vacation where you expect to drive approximately 2,000 miles round trip. Therefore, the total distance driven in a year, including the vacation, is:
- [tex]\( 8,160 \, \text{miles (work)} + 2,000 \, \text{miles (vacation)} = 10,160 \, \text{miles/year} \)[/tex]
### Step 4: Determine if you stay under the mileage restriction if leasing.
The mileage restriction for the lease is 10,000 miles per year. Since your total expected distance driven in a year, including the vacation, is 10,160 miles, this exceeds the mileage restriction.
Thus, you will not stay under your mileage restriction if leasing.
### Summary
You live 17 miles from work. You can expect to drive a minimum of 170 miles per week. You will work about 48 weeks per year, so you can expect to drive a minimum of 8,160 miles per year for work. You have a vacation planned and you expect to drive approximately 2,000 miles round trip. If you take the vacation, you will not stay under your mileage restriction if leasing.
