Understanding Calculus

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  Home
  Testimonials
  Table of Contents

  Preface
  1. Why Study
  Calculus
  2. Numbers
  3. Functions
  4. The Derivative
  5. Differentiation
  6. Applications
  7. Free Falling
  Motion
  8. Understanding
  Derivative
  9. Derivative
  Approximations
  10. Integration
  Theory
  11. Understanding
  Integration
  12. Differentials

  Inverse Functions
  Exponents
  Exponential
  Functions
  Applications of
  Exponential
  Functions
  Sine and Cosine
  Function
  Sine Function
  Sine Function -
  Differentiation and
  Integration
  Oscillatory Motion
  Mean Value
  Theorem
  Taylor Series
  More Taylor Series
  Integration
  Techniques

  Links
  Contact

 
 
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CHAPTER 3

Chapter 3 - The Mathematical function and its Graph

Gas savings calculator

The savings of driving slower expressed in dollars per hour

Most 4-cylinder japaneese/korean cars achieve maximum fuel efficiency at 45 miles per hour. Most drivers average 70 miles per hour on the interstate. If they drove 55 instead of 70, they would observe 15% better gas mileage. The problem is drivers do not think the extra time it takes by driving slower is worth the gas savings.

In this exercise we will develop a function to express the savings in terms of dollars per hour. So if someone who drives 55 takes 1 hour longer to reach their destination, we can say they saved $x per hour. If they took 3 hours longer, their total savings would be 3 * $x. So you can compare that number to the minimum wage to determine if their time was better spent flipping burgers or driving slower.

Speed 1
Gas mileage at speed 1 ( miles/gallon )
Speed 2
Gas mileage at speed 2 ( miles/gallon )
Cost per gallon of gas
Cost savings per hour

You have to look at the problem in terms of how much longer you are spending in the car relative to the higher speed. So if it takes 1 hour at 70 mph to do 70 miles it takes 1 hour 16 minutes to do it at 55 mph. So you have to take the fuel savings for that trip and divide it by 16 minutes to get your $savings/hour.

Doing this we get:

At 70 mph, mileage is 35 mpg , so 2 gallons of gas is used. At $3.85/gallon will have spent $7.7

At 55mph, mileage is 41 mpg, so we spent ( 70/41 ) * 3.85 = $6.60

So for 16 minutes longer trip we saved $7.70 - $6.60 or $1.10 which translates to hourly savings of $1.10 / 16 minutes = $4.1/hour

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