SOLUTION: A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost $3.50 per gallon. For each mile per hour increase i

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Question 503468: A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost $3.50 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage. Driver gets $27.50 per hour in wages and fixed cost for running the truck amount to $11.33 per hour. What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip?
A. Let's start out by finding how long the trip will take?
B. Now, with this time known, how much will it cost to pay the driver and run the truck?
I need help with just setting up the problem and doing A and B, this is a huge math project and I think If i can have help with the first couple few I can do the rest.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost $3.50 per gallon.
For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage.
Driver gets $27.50 per hour in wages and fixed cost for running the truck amount to $11.33 per hour.
What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip?
;
A. Let's start out by finding how long the trip will take?
= 5.2 hrs to make the 260 mi trip at 50 mph
:
B. Now, with this time known, how much will it cost to pay the driver and run the truck?
5.2 * 27.50 = $143.00, for the driver
5.2 * 11.33 = $58.92, for the truck
----------------------
total cost: $201.92
:
Cost for gas: * 3.50 = $130.00 for gas (at 50 mph)
add to the above cost: 201.92 + 130 = $331.92 total for the 260 mi trip
:
Correct a math error above, but also:
:
"What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip? :
Speed affects time which affects cost
Speed also affect gas mileage
let s = speed
then
= time
and
= amt of gas required
:
Write a cost equation which is in terms of speed (s)
Cost = driver time + truck time + gas used
C(s) = *27.50 + *11.33 + *3.50