To find out when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation based on their weekly gas usage and their starting amounts of gas.
Let's define:
- Miguel's starting amount of gas: \( G_m = 20 \) gallons (full tank)
- Christina's starting amount of gas: \( G_c = 16 \) gallons (full tank)
- Miguel's gas usage per week: \( U_m = 1.5 \) gallons/week
- Christina's gas usage per week: \( U_c = 1 \) gallon/week
After \( t \) weeks, the amount of gas in their tanks will be:
For Miguel: \[ G_m(t) = 20 - 1.5t \]
For Christina: \[ G_c(t) = 16 - 1t \]
We want to find \( t \) when \( G_m(t) = G_c(t) \):
\[ 20 - 1.5t = 16 - 1t \]
Now, solve for \( t \):
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Add \( 1.5t \) to both sides: \[ 20 = 16 - 1t + 1.5t \] \[ 20 = 16 + 0.5t \]
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Subtract 16 from both sides: \[ 20 - 16 = 0.5t \] \[ 4 = 0.5t \]
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Divide both sides by 0.5: \[ t = \frac{4}{0.5} = 8 \]
Thus, after 8 weeks, Miguel and Christina will have the same amount of gas in their tanks.
The answer is: • After 8 weeks they will have the same amount of gas in their tanks.