Chapter 5, Problem 53RE

(a)

To determine

To approximate the total fuel consumption during the hour by using Trapezoidal rule.

Answer to Problem 53RE

The total fuel consumption during the hour is 2.42 gallons approximately.

Explanation of Solution

Given: During a trip, a passenger recorded the fuel consumption every 5 minutes for a full hour of travel

  

Calculation: Using Trapezoidal rule,

  $T=\frac{h}{2}\left[y_0+2\left(y_1+\mathrm{....}+y_{n-1}\right)+y_n\right]$

where $h=5\text{ minutes or }h=\frac{1}{12}\text{ hours}$ is the time interval. Therefore

  $\begin{array}{l}T=\frac{1}{2\times 12}\left[2.5+2\left(2.4+\mathrm{....}+2.4\right)+2.3\right]\\ T=\frac{1}{24}\left[2.5+2\left(26.6\right)+2.3\right]\\ T=\frac{1}{24}\left[58\right]\\ T=2.42\text{ gallons}\end{array}$

Conclusion: Therefore, the total fuel consumption during the hour is 2.42 gallons approximately.

(b)

To determine

To determine the fuel efficiency of automobile.

Answer to Problem 53RE

The fuel efficiency is 24.83 miles per gallon for the portion of trip.

Explanation of Solution

Given: An automobile covered 60 miles in the hour and total fuel consumption during the hour is 2.42 gallons.

Calculation: The fuel efficiency is given by formula

  $\begin{array}{l}\text{Fuel efficiency}=\frac{\text{distance covered in one hour}}{\text{total fuel consumption in one hour}}\\ \text{Fuel efficiency}=\frac{\text{60}}{\text{2}\text{.42}}\\ \text{Fuel efficiency}=\text{24}\text{.83 miles per gallon}\\ \end{array}$

Conclusion: Thus, the fuel efficiency is 24.83 miles per gallon.