Question

If there are approximately 1.8 million cars in Vancouver and if each car travels an average of 17,500 kilometres in a year, how much gasoline is used per year for all of the cars, assuming an average gas mileage of 40 miles per gallon? Provide your answer in litres in scientific notation to 2 decimal places. Show all your work.

Answer 1

Rates are used to measure a quantity over another.

The 1.8 million cars use $1.85 \times 10^{10}$ liters each year

Given

$Cars = 1.8\ million$

$d = 17500km$ --- distance

$r = 40miles/gallon$

First, we calculate the number (n) of gallons used by each car

$r = \frac{d}{n}$

Solve for n

$n = \frac{d}{r}$

So, we have:

$n = \frac{17500km}{40miles/gallon}$

$n = \frac{17500km}{40miles}gallon$

Convert miles to kilometers

$n = \frac{17500km}{40km \times 1.60934}gallon$

$n = \frac{17500km}{64.3738km}gallon$

$n = 271.85\ gallon$

The number of gallons (N), used by all the cars is:

$N = n \times cars$

$N = 271.85 \times 1.8\ million$

$N = 489330000$

Convert to liters

$N = 489330000 \times 3.78541L$

$N = 1852314675.3L$

In scientific notation to 2 decimal places, we have:

$N = 1.85 \times 10^{10}L$

Hence, the number of liters used is $1.85 \times 10^{10}$

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