Chapter 1.5, Problem 27HP

a

To determine

To test: Whether the fuel economy rating of a new car is accurate.

Answer to Problem 27HP

Explanation of Solution

Given Information:EPA has a complex way to determine the fuel economy data for a car.

Formula used:

  $CombinedMPG=\frac{1}{\frac{0.55}{CITY}+\frac{0.45}{HWY}}$ -(i)

Calculation:

During the experiment, an adult drove car in city for $2.5miles$ , about $0.1gallon$ of fuel was depleted.

Ratings in city (CITY) $=\frac{2.5}{0.1}=25mpg$

Also, the adult drove car in city for $3miles$ , about $0.1gallon$ of fuel was depleted.

Ratings on highway (HWY) $=\frac{3}{0.1}=30mpg$

So, CITY $=25mpg$ and HWY $=30mpg$ .

Putting these values in (i),

  $CombinedMPG=\frac{1}{\frac{0.55}{25}+\frac{0.45}{30}}$ $=\frac{1}{\frac{0.55}{25}+\frac{0.45}{30}}=\frac{1}{0.037}=27.027$

Also, the certified fuel economy rating received from the company was $27.$

So, the rating from the company is accurate.

b.

To determine

To calculate: The combined miles per gallon for a car with given ratings.

Answer to Problem 27HP

  $CombinedMPG=32.0616$

Explanation of Solution

Given Information:

CITY $=30mpg$ -(i)

HWY $=35mpg$ -(ii)

Formula used:

  $CombinedMPG=\frac{1}{\frac{0.55}{CITY}+\frac{0.45}{HWY}}$ -(iii)

Calculations:

Using (i) and (ii) in (iii),

  $CombinedMPG=\frac{1}{\frac{0.55}{30}+\frac{0.45}{35}}$ $=\frac{1}{0.01833+0.01286}$ $=\frac{1}{0.03119}$ $=32.0616$

Thus, $CombinedMPG=32.0616$ .