Question

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.

Answer 1

Answer:70 mph

Explanation:

70 mph yields better income for him since:

At 70mph he arrives in 6hrs and makes $300

Minus 420/24 = $74.25 in costs

He makes $225.25

While he makes $220.5 at 60mph( after calculations like the above)

Answer 2

Answer:

Now here two options available to Darius. Option one is to drive at 70mph and option 2 is to drive at 60mph

Option 1: 70mph

Winning price at arrival in 6 hours (70mph avg speed)                $300

Cost of gasoline= Number of gallons used (W1) * Price per gallon

Cost of gasoline= 17.5 gallons * $4.25=                                       ($74.375)

Net Savings                                                                                   $225.625

Option 2: 60mph

Winning price at arrival in 7 hours (60mph avg speed)                $280

Cost of gasoline= Number of gallons used (W2) * Price per gallon

Cost of gasoline= 14 gallons * $4.25=                                         ($59.5)

Net Savings                                                                                  $220.5

As the net saving is higher in the option 1, hence the best option here for Darius is to drive at 70mph to maximise his winnings.

Explanation:

Working 1:

Number of gallons used= Total miles / Gallons per mile usage at 70mph

Number of gallons used=420/24=17.5 gallons

Working 2:

Number of gallons used= Total miles / Gallons per mile usage at 60mph

Number of gallons used=420/30=14 gallons