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Homework answers / question archive / 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

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.

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Case 1: The price of gasoline is $4.25 and speed is 70 mph.

Distance covered in 1 gallon at a speed of 70mph is 24 miles.

So, total gasoline fuel cost is:

C=42024×4.25=74.375C=42024×4.25=74.375

The winning price is 300.

The total money won excluding the fuel cost is:

M=300−74.375=225.625M=300−74.375=225.625

Case 2: The price of gasoline is 4.25 and speed is 60 mph.

Distance covered in 1 gallon at a speed of 60mph is 30 miles.

So, total gasoline fuel cost is:

C=42030×4.25=59.5C=42030×4.25=59.5

The winning price is 280.

The total money won excluding the fuel cost is:

M=280−59.5=220.5M=280−59.5=220.5

The money won when Darius drives at 70 mph is 225.625 whereas at 60 mph is 220.5. So, Darius should drive at 70 miles per hour.

Case 3: The price of gasoline is 6.90 and speed is 70 mph.

Distance covered in 1 gallon at a speed of 70mph is 24 miles.

So, total gasoline fuel cost is:

C=42024×6.90=120.75C=42024×6.90=120.75

The winning price is 300.

The total money won excluding the fuel cost is:

M=300−120.75=179.25M=300−120.75=179.25

Case 4: The price of gasoline is 6.90 and speed is 60 mph.

Distance covered in 1 gallon at a speed of 60mph is 30 miles.

So, total gasoline fuel cost is:

C=42030×6.90=96.6C=42030×6.90=96.6

The winning price is 280.

The total money won excluding the fuel cost is:

M=280−96.6=183.4M=280−96.6=183.4

The money won when Darius drives at 70 mph is 179.25 whereas at 60 mph is 183.4. So, Darius should drive at 60 miles per hour.

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