Q39P - Fundamentals Of Physics

Question

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car’s fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon: 

    $\mathbf{1}\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{gallon}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{546}\mathbf{ }\mathbf{090}\mathbf{ }\mathbf{0}\mathbf{ }\mathbf{liters}$

    $\mathbf{1}\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{gallon}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{785}\mathbf{ }\mathbf{411}\mathbf{ }\mathbf{8}\mathbf{ }\mathbf{liters}$

For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

Step-by-Step Solution

Answer

1. The amount of fuel that the tourist mistakenly believes she needs is 18.8 gallons (as per the UK system).

2. The amount of fuel that the tourist’s car actually takes is 22.5 gallons (as per the US system).

Step 1: Given data

The trip of tourist is ${}^{\mathbf{750}\mathbf{ }\mathbf{miles}}$ (in the US).

Fuel consumption rate of the car is ${}^{\mathbf{40}\mathbf{ }\mathbf{gallons}\mathbf{ }\mathbf{per}\mathbf{ }\mathbf{mile}}$

$\mathbf{1}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{ }\mathbf{gallon}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5460900}\mathbf{ }\mathbf{liters}$

$\mathbf{1}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{gallon}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{7854118}\mathbf{ }\mathbf{liters}$

Step 2: Understanding the Understanding the relationship between U.K. gallon and U.S. gallon.

In this problem the ratio of the 1 U.K. gallon and the 1 U.S. gallon can be found to measure the amount of fuel.

$\mathbf{1}\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{ }\mathbf{gallon}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5460900}\mathbf{ }\mathbf{liter}\mathbf{\times }\frac{\mathbf{1}\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{gallon}}{\mathbf{3}\mathbf{.}\mathbf{78}\mathbf{ }\mathbf{liter}}$

$\mathbf{1}\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{ }\mathbf{gallon}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{u}\mathbf{.}\mathbf{s}\mathbf{.}\mathbf{ }\mathbf{gallon}$

Step 3: (a) Determination of the amount of fuel that the tourist mistakenly believes she needs

Amount of fuel consumed by car for the trip is${}^{\left(\frac{\mathrm{Actual} \mathrm{distance}}{\mathrm{Fuel} \mathrm{consumption} \mathrm{rate} \mathrm{of} \mathrm{car}}\right)}$

The tourist travels${}^{\mathbf{750}\mathbf{ }\mathbf{miles}}$ by car that has fuel consumption capacity as${}^{\mathbf{40}\mathbf{ }\mathbf{gallons}\mathbf{ }\mathbf{per}\mathbf{ }\mathbf{mile}\mathbf{ }}$.

So, the amount of fuel that the tourist believes she needs is, 

$$\begin{gathered} \frac{\mathbf{Actual}\mathbf{ }\mathbf{distance}}{\mathbf{Fuel}\mathbf{ }\mathbf{consumtion}\mathbf{ }\mathbf{rate}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{cae}}\mathbf{=}\frac{\mathbf{750}}{\mathbf{40}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{18}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{gallon} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{18}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{gallons}\mathbf{ }\mathbf{(}\mathbf{In}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{)} \end{gathered}$$

Step 4: (b) Determination of the amount of fuel in US Gallons that the tourist’s car actually takes

As you know the relation between U.S. Gallon and U.K. Gallon, you can find the amount of fuel that the tourist actually requires for a trip in U.S Gallon.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{K}\mathbf{.}\mathbf{ }\mathbf{gallon}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{Gallon} \\ \mathbf{18}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{UK}\mathbf{ }\mathbf{Gallon}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{18}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{UK}\mathbf{ }\mathbf{Gallon}\mathbf{\times }\frac{\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{Gallon}}{\mathbf{1}\mathbf{ }\mathbf{ }\mathbf{UK}\mathbf{ }\mathbf{Gallon}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{22}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{Gallons} \end{gathered}$$

Thus, the car actually takes ${}^{\mathbf{22}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{U}\mathbf{.}\mathbf{S}\mathbf{.}\mathbf{ }\mathbf{Gallons}}$ .