12.065 Map scales

Lesson

Speed, distance and time formulas

Speed

$\text{average speed}=\frac{\text{total distance travelled}}{\text{total time taken}}$average speed=total distance travelledtotal time taken

$S=\frac{D}{T}$S=DT

Time or distance
Finding unknown time or distance:
Unknown time Unknown distance
$T=\frac{D}{S}$T=DS $D=S\times T$D=S×T

Map scales

To create maps, building plans, and other technical drawings, the features being represented must be scaled down to fit on the piece of paper, and we express this scaling factor with a ratio. For example, if a small city is $100000$100000 times larger than a piece of paper, scaling its features down onto a map drawn on that paper would have the scaling ratio of $1:100000$1:100000, meaning $1$1 cm measured on the map represents $100000$100000 cm (or $1$1km) in real life.

Another way to represent the distances on a map or building plan is to use a scale bar. This small bar on the drawing shows the corresponding distance in real life. On a map, a scale bar might measure $10$10 cm long, but if it is labelled as $20$20 km we know that if two features are $10$10 cm apart on the map then they are $20$20 km apart in real life.

Practice question

Question 1

Carl wanted to fly from Perth to Adelaide with an overnight stop in Sydney.

1. Carl's first plane took $4$4 hours of flight time. If the airplane was travelling at an average speed of $825$825 km/h, what is the distance between Perth and Sydney as it appears on the map, measured in scaled units on the map?

Give your answer to one decimal place.

2. Carl's second trip took $2.2$2.2 hours. If the distance between Sydney and Adelaide appears to be $2.2$2.2 units on the map, what was the average speed of the airplane? Give your answer to the nearest integer.

3. Carl's overnight stay at a hotel in Sydney costs 120$120. If the flight company charges$11\$11 cents/km for the flight, what was the total cost of the trip?

Give your answer to the nearest cent.

Outcomes

ACMEM086

calculate speed, distance or time using the formula speed = distance/time

ACMEM087

calculate the time or costs for a journey from distances estimated from maps

ACMEM089

calculate and interpret average speed; for example, a 4-hour trip covering 250 km