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Darius has entered a competition in which he must drive from his home town of Memphis Tennessee to New Orleans Louisiana, a distance of approximately 420 miles

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Darius has entered a competition in which he must drive from his home town of Memphis Tennessee to New Orleans Louisiana, a distance of approximately 420 miles. If he arrives in 6 hours (an average speed of 70 mph) he will receive a prize of $300. If he arrives in 7 hours (an average speed of 60 mph), he receives $280. One of the competition rules is he must pay for his own gasoline and Darius has calculated that he averages 24 miles per gallon at 70 mph and 30 miles per gallon at 60 mph.

To maximize his winnings (prize money minus the cost of gasoline) at what speed should Darius drive if the price of gasoline is $4 25 per gallon? Darius Should drive at _____ miles per hour.

Alternatively, if the price of gasoline is $6 90 per gallon then Darius should drive at _____ miles per hour.