Aaah difficult problem!

algaljal

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Oct 7, 2009
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Here's my question :

A driver on a desert road discovers a hole in the gas tank leaking gas at the constant rate of 4 gallons per hour. This driver, having no way to plug the hole, decides to drive for as long as the gas supply allows. The gauge reading indicates the tank is three-fourths full, which means that the tank contains 14 gallons. The car consumes gas at the rate of 18 miles per gallon at 40 mpg. For each 5 mpg below 40 mpg add one-half mile per gallon to this rate; for each 5 mpg above 40 mpg, subtract one mile per gallon from this rate. If the driver chooses the best constant speed in order to get the maximum driving distance, find the maximum distance that the 14 gallons will allow. Assume that gas consumption is a continuous functional speed.

I have no idea how to start, help please?
 
algaljal said:
Here's my question :

A driver on a desert road discovers a hole in the gas tank leaking gas at the constant rate of 4 gallons per hour. This driver, having no way to plug the hole, decides to drive for as long as the gas supply allows. The gauge reading indicates the tank is three-fourths full, which means that the tank contains 14 gallons. The car consumes gas at the rate of 18 miles per gallon at 40 mpg. For each 5 mpg below 40 mpg add one-half mile per gallon to this rate; for each 5 mpg above 40 mpg, subtract one mile per gallon from this rate. If the driver chooses the best constant speed in order to get the maximum driving distance, find the maximum distance that the 14 gallons will allow. Assume that gas consumption is a continuous functional speed.

I have no idea how to start, help please?

First start naming variables.

What is that you want find - the maximum distance that the 14 gallons will allow

let

maximum distance = M

The car consumes gas at the rate of 18 miles per gallon at 40 mpg. Is that mpg or mph?

Please show us your work, inidcating exactly where you are stuck - so that we know where to begin to help you.
 
algaljal said:
at 40 mph
-still stuck at the very beginning

You have many more mistakes in your problem statement. Please fix those - otherwise no rigourous solution possible.... only guesses
 
Ok, the tank is leaking 4 gal per hr. and you have 14 gals. in the tank.

Hence if you didn't go anywhere, in 3.5 hrs. you would be out of gas.

Now the faster you go, the less gas you used, for example if you go 80 mph you will used 13.71 gallons in two hours (including leakage) and will have gone a distance of 160 miles with .29 gallons still left in your tank.

This looks like a problem for Solve on Excel, do you have the Excel program on your computer?

Note: This problem could be solved by the process of elimination, but that involves a lot of grunt work, which I''l leave to the computer.
 
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