Question

Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point) Responses After 1.6 weeks they will have the same amount of gas in their tanks. After 1.6 weeks they will have the same amount of gas in their tanks. After 8 weeks they will have the same amount of gas in their tanks. After 8 weeks they will have the same amount of gas in their tanks. After 1/8 week they will have the same amount of gas in their tanks. After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks. After −8 weeks they will have the same amount of gas in their tanks.

Answer 1

To find when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation based on their rates of gas usage.

Let \( t \) be the number of weeks.

1. Initial Amount of Gas:

   • Miguel has a 20-gallon capacity and uses 1.5 gallons per week, so if he starts full: \[ \text{Gas in Miguel's tank after } t \text{ weeks} = 20 - 1.5t \]

   • Christina has a 16-gallon capacity and uses 1 gallon per week. If she starts full: \[ \text{Gas in Christina's tank after } t \text{ weeks} = 16 - 1t \]

2. Setting the Equations Equal: We want to find \( t \) when the amounts of gas in their tanks are the same: \[ 20 - 1.5t = 16 - 1t \]

3. Solving the Equation: Rearranging gives: \[ 20 - 16 = 1.5t - 1t \] \[ 4 = 0.5t \] \[ t = \frac{4}{0.5} = 8 \]

Therefore, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.