To find out when Miguel and Christina will have the same amount of gas in their tanks, we need to set up the equations for the amount of gas each person has over time.
Let \( t \) be the time in weeks.
- Miguel's car starts full with 20 gallons and uses 1.5 gallons per week. Thus, the amount of gas Miguel has after \( t \) weeks can be expressed as:
\[ \text{Miguel's gas} = 20 - 1.5t \]
- Christina's car starts full with 16 gallons and uses 1 gallon per week. Therefore, the amount of gas Christina has after \( t \) weeks can be expressed as:
\[ \text{Christina's gas} = 16 - 1t \]
To find when they have the same amount of gas, we set the two equations equal to each other:
\[ 20 - 1.5t = 16 - 1t \]
Now, we can solve for \( t \):
- Add \( 1.5t \) to both sides:
\[ 20 = 16 - 1t + 1.5t \]
- This simplifies to:
\[ 20 = 16 + 0.5t \]
- Subtract 16 from both sides:
\[ 4 = 0.5t \]
- Multiply both sides by 2:
\[ t = 8 \]
Thus, after 8 weeks, Miguel and Christina will have the same amount of gas in their tanks.
The correct answer is:
After 8 weeks they will have the same amount of gas in their tanks.