Darius has entered a competition in which he must drive from his home town of memphis comma tennessee to new orleans comma louisianaâ, a distance of approximately 420 miles. if he arrives in 6 hoursâ (an average speed of 70â mph), he will receive a prize of â$300. if he arrives in 7 hoursâ (an average speed of 60â mph), he receives â$280. one of the competition rules is he must pay for his ownâ gasoline, and darius has calculated that he will average 24 miles per gallon at 70 mph and 30 miles per gallon at 60 mph.
1. to maximize his winningsâ (prize money minus the cost ofâ gasoline), at what speed should darius drive if the price of gasoline is $ 4.25 perâ gallon?
2. âalternatively, if the price of gasoline is $ 6.90 perâ gallon, then darius should drive at miles per hour.
3. at what gasoline price would darius be indifferent to arriving in either 6 hours or 7 hours if he wants to maximize hisâ winnings?