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

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.