Question

A US gallon is 231 cubic inches. An Imperial gallon, often used in England and other British Commonwealth countries, is 277.42 cubic inches. Note that 1 inch = 2.54 cm (exactly). a. Say that on a particular day, gasoline in Great Falls, Montana is selling for 3.50 USD per US gallon. At the same time, gasoline in Lethbridge, Alberta is 5.00 CAD per Imperial gallon. If 1.00 CAD = 0.75 USD, on which side of the border is gas cheaper? Start by converting both prices to CAD per litre (1 L = 1000 cubic centimetres). Remember to show all of your work! (8) b. If you are driving down to Great Falls (perhaps to buy gas?) at 110 km/h, how fast are you going in miles per hour (mph) and metres per second?

Answer 1

Given : 1 US gallon = 231 in3 , 1 imperial gallon = 277.42 in3 , 1 in= 2.54 cm,

Price of gasoline at Great falls, Montana : 3.50 USD per US gallon
Price of gasoline at Lethbridge, Alberta : 5 CAD per imperial gallon
Solution:

(a)

We know that , 1 L = 1000 cm3 , 1 in = 2.54 cm

1 US gallon = 231 in3 = 231×(2.54)3 cm3 = 3785.41 cm3

So , 1 US gallon = 3.785 L

1 imperial gallon (British) = 277.42 in3 = 277.42×(2.54)3= 4546.099 cm3

So in litres, 1 Imperial gallon = 4.546 L

Now , 1 US gallon (USA Montana) = 231 in3 = 231×(2.54)3= 3785 cm3

So in litres, 1 US gallon = 3.785 L

For Great falls, Montana

3.50 USD per US gallon = 3.50*(1/0.75) CAD per US gallon = 4.67 CAD/US gallon

Now 4.67 CAD/US gallon =( 4.67/3.785) CAD per liter

= 1.23 CAD per liter

For Lethbridge , Alberta

5 CAD per imperial gallon = (5/4.546) CAD per liter

= 1.1 CAD per liter

Answer : The gas is cheaper in Lethbridge, Alberta

(b)

1 km= 1000 m and 1 h = 3600 s

So, 1 km/h = (1000/3600) m/s = 0.278 m/s

So, 110 km/h = 110*0.278 = 30.58 m/s

1 km = 0.621 mile

So 1 km/h = 0.621 mile per hour

So 110 km/h = 110*0.621 mile per hour = 68.31 miles per hour

Answer: 68.31 miles per hour and 30.58 m/s