1. **State the problem:** We have two cars, Ahmad's and Greg's, with gas tanks decreasing as miles are driven. Ahmad's starts with about 26 gallons and runs out at 360 miles. Greg's starts with about 12 gallons and runs out at 600 miles. 2. **Find the gas remaining after 150 miles for each car:** - Ahmad's car decreases steeply from 26 gallons to 0 gallons over 360 miles. - Greg's car decreases gradually from 12 gallons to 0 gallons over 600 miles. 3. **Calculate the rate of gas consumption for each car:** - Ahmad's rate: $$\text{rate}_A = \frac{26 - 0}{0 - 360} = \frac{26}{360} \approx 0.0722 \text{ gallons per mile}$$ - Greg's rate: $$\text{rate}_G = \frac{12 - 0}{0 - 600} = \frac{12}{600} = 0.02 \text{ gallons per mile}$$ 4. **Calculate gas remaining after 150 miles:** - Ahmad's gas: $$26 - 0.0722 \times 150 = 26 - 10.83 = 15.17 \text{ gallons}$$ - Greg's gas: $$12 - 0.02 \times 150 = 12 - 3 = 9 \text{ gallons}$$ 5. **Answer (a):** After 150 miles, Greg's car has less gas remaining. - Difference: $$15.17 - 9 = 6.17 \text{ gallons}$$ 6. **Find when the tanks contain the same amount of gas:** Set gas remaining equal: $$26 - 0.0722x = 12 - 0.02x$$ Solve for $x$: $$26 - 12 = 0.0722x - 0.02x$$ $$14 = 0.0522x$$ $$x = \frac{14}{0.0522} \approx 268.58 \text{ miles}$$ 7. **Answer (b):** The tanks contain the same amount of gas after approximately 269 miles. 8. **If miles driven is less than 269, which car has less gas?** - Since Ahmad's gas decreases faster, Ahmad's car will have less gas remaining before 269 miles. **Final answers:** (a) Greg's car has less gas after 150 miles by approximately 6.17 gallons. (b) Tanks have the same gas at about 269 miles. Before this, Ahmad's car has less gas.