SOLUTION: I REALLY don't know how to get the equations from this problem: Here are some facts about semi-trucks and a trip between Chicago and New Orleans. (a) The trip is 750 miles

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Question 919819: I REALLY don't know how to get the equations from this problem:
Here are some facts about semi-trucks and a trip between Chicago and
New Orleans.
(a) The trip is 750 miles.
(b) Running at 50 mph, the truck gets around 4 miles per gallon.
(c) For each mph increase in speed, the truck losses 1/10 of a mile per
gallon in mileage.
(d) The driver team gets $27 per hour.
(e) Keeping the truck on the road costs 15 dollars per hour over and
above the cost of fuel.
(f) Diesel fuel costs $3.90 per gallon.
-Write a function, C(x), for the total cost of driving the truck from Chicago to New Orleans in terms of the CONSTANT speed x.
-At what (constant) speed should the truck be driven to minimize the cost of the trip? Use calculus to minimize costs.
Thank you so much for your help!
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The key to this is buried in the data
The total time spent on the road is:
( distance traveled ) / ( constant speed )

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The mi/gal that the truck gets is:

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I can say:
( $ / gal ) / ( mi / gal ) = $ / mi

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( $ / mi )*( mi ) = $

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Now I can say:

Multiply top and bottom of first term by

This checks out for
If you agree with my steps, you can do the calculus
Strange that if the truck goes 90 mi/hr or doesn't
move at all, the cost is infinite!
Hope this helps