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?
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A. Let's start out by finding how long the trip will take?
{{{260/50}}} = 5.2 hrs to make the 260 mi trip at 50 mph
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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
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total cost:  $201.92 
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Cost for gas: {{{260/7}}} * 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
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Correct a math error above, but also:
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"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
{{{260/s}}} = time
and
{{{260/(7-.1(s-50))}}} = amt of gas required 
:
Write a cost equation which is in terms of speed (s)
Cost = driver time + truck time + gas used
C(s) = {{{260/s}}}*27.50 + {{{260/s}}}*11.33 + {{{260/(7-.1(s-50))}}}*3.50