To estimate the amount of gas she needs, Felicia calculates the distance traveled at 70 mph for 1.25 hours. She might calculate \)$70\cdot 1.25 = 70 + 0.25\cdot 70 = 70 + 17.5 = 87.5 \mbox{ miles}.$$ Since 1 gallon of gas will take her 30 miles, 3 gallons of gas will take her 90 miles, a little more than she needs. So she might figure that 3 gallons is enough.
Or, since she is driving, she might not feel like distracting herself by calculating \(0.25\cdot70\) mentally, so she might replace \(70\) with \(80\), figuring that that will give her a larger distance than she needs. She calculates $$80\cdot 1.25 = 80+ \frac14 \cdot 80 = 100.$$ So at 30 miles per gallon, \(3 \frac13\) gallons will get her further than she needs to go, so should be enough to get her to the gas station.
Commentary
This task provides students the opportunity to make use of units to find the gas need (N-Q.1). It also requires them to make some sensible approximations (e.g., 2.92 gallons is not a good answer to part (a)) and to recognize that Felicia's situation requires her to round up. Various answers to (a) are possible, depending on how much students think is a safe amount for Felicia to have left in the tank when she arrives at the gas station. The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.