Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 1 - Measurement - Problems: 39b

Answer

The 750 mile trip requires 22.51781 U.S. gallons

Work Step by Step

If you did part a) you can use that number to solve the problem through dimensional analysis. Just take the number of gallons she thinks she needs (answer to part a), and convert them to U.S. gallons. 18.75 U.K. gallons * $\frac{4.5460900}{1}$$\frac{liters}{U.K.gallon}$ * $\frac{1}{3.7854118}$$\frac{U.S. gallon}{liters}$ = 22.51781 U.S. gallons If you didn't do part a) you can still solve this problem by using dimensional analysis. Start off with the 40 miles per U.K. gallon, and convert it to what the car actually gets in miles per U.S. gallon. Then we can figure out the U.S. gallons required from there. 40$\frac{miles}{U.K.gallon}$ * $\frac{1}{4.5460900}$$\frac{U.K.gallon}{liters}$ * $\frac{3.7854118}{1}$$\frac{liter}{U.S.gallon}$ = 33.30697$\frac{miles}{U.S.gallon}$ This is in miles per U.S. gallon, but we just want to know how many U.S. gallons the car actually requires. We can find this by dividing the miles planned on traveling the miles per U.S. gallon. Notice how the units flip, this is because we are actually dividing by the miles per U.S. gallon, in order to obtain the correct unit through dimensional analysis. 750 miles * $\frac{1}{33.30697}$$\frac{U.S. gallon}{miles}$ = 22.51781 U.S. gallons
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