For speeds between 40 mph and 65 mph, a diesel truck gets 460x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 4.6 dollars per gallon. The driver is paid 23 dollars per hour.
a) What is the total cost to have the truck driven 200 miles at a constant speed of 50 miles per hour?
b) What is the best constant speed to drive the truck to minimize the total cost to drive it 200 miles?
c) How much money is saved, per 200 miles, by driving at the the constant speed you found in problem B) instead of 50 miles per hour?
take a look at your other trucking post. This is basically the same.
To solve this problem, we need to follow these steps:
Step 1: Calculate the number of gallons consumed to cover a specific distance for each speed.
Step 2: Calculate the cost of gasoline for each speed.
Step 3: Calculate the driver's pay for the time it takes to cover the distance at each speed.
Step 4: Calculate the total cost for each speed.
Step 5: Compare the costs for different speeds to answer the questions.
a) Total cost to have the truck driven 200 miles at a constant speed of 50 miles per hour:
Step 1: To calculate the number of gallons consumed, we divide the distance by the speed:
Number of gallons consumed = Distance / Speed
Number of gallons consumed = 200 miles / 50 mph = 4 gallons
Step 2: We multiply the number of gallons consumed by the cost of gasoline per gallon:
Gasoline cost = Number of gallons consumed * Cost per gallon
Gasoline cost = 4 gallons * $4.6/gallon = $18.4
Step 3. We calculate the driver's pay for the time taken to cover the distance:
Driver's pay = Time * Pay per hour
Time = Distance / Speed
Time = 200 miles / 50 mph = 4 hours
Driver's pay = 4 hours * $23/hour = $92
Step 4: We sum up the gasoline cost and driver's pay to get the total cost:
Total cost = Gasoline cost + Driver's pay
Total cost = $18.4 + $92 = $110.4
Therefore, the total cost to have the truck driven 200 miles at a constant speed of 50 miles per hour is $110.4.
b) The best constant speed to minimize the total cost to drive the truck 200 miles:
To find the best constant speed, we need to compare the costs of different speeds for driving 200 miles.
We can repeat the steps above for speeds between 40 mph and 65 mph.
For each speed, calculate the total cost using the same steps as in part a). Record the costs for each speed.
By comparing the costs, we can determine the speed that results in the lowest total cost.
c) The amount of money saved, per 200 miles, by driving at the constant speed found in part b) instead of 50 miles per hour:
To calculate the savings, subtract the total cost at the constant speed found in part b) from the total cost at 50 miles per hour, which was calculated in part a).
Savings = Total cost (50 mph) - Total cost (speed found in part b))
By calculating the savings, you can determine how much money is saved per 200 miles by driving at the constant speed found in part b) instead of 50 miles per hour.