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12.065 Map scales

Worksheet
Map scales
1

Vincent took a car trip from Pittsburgh to Baltimore. The driving time was 2.9 hours. If the distance between Pittsburgh and Baltimore is 2.8 units as it appears on the map, what is the average speed of the car? Round your answer to two decimal places.

2

Ned took a plane from Brisbane to Townsville. The flight time was 2.4 hours. If the distance between Brisbane and Townsville is 4 units as it appears on the map, what is the average speed of the airplane? Round your answer to two decimal places.

3

Harry took a car trip from Tampere to Kotka. The driving time was 2.5 hours. If the distance between Tampere and Kotka is 1.8 units as it appears on the map, what is the average speed of the car?

4

Justin took an airplane from Lusaka to Durban. The flight time was 3.3 hours. If the distance between Lusaka and Durban is 2.7 units as it appears on the map, what is the average speed of the airplane? Round the answer to the nearest whole number.

5

Abdul is driving from Perth to Coral Bay:

a

Given the scale on the map, estimate the distance from Perth to Coral Bay correct to the nearest 100 \text{ km}.

b

If the car consumes 13 litres per 100 \text{ km}, estimate how much fuel will be used during the drive.

c

If fuel costs \$1.35 per litre, estimate the cost of fuel for the drive.

d

If the car travels at an average of 100\text{ km/h}, how long will the trip take in hours?

6

Consider the following map:

a

Given the scale on the map, estimate the distance from Adelaide to Uluru correct to the nearest 100 \text{ km}.

b

If the car consumes 12 litres per 100 \text{ km}, estimate how much fuel will be used during the drive.

c

If fuel costs \$1.40 per litre, estimate the cost of fuel for the trip.

d

If the car travels at an average of 95\text{ km/h}, estimate how long the trip will take in hours.

7

Consider the following map:

a

Given the scale on the map, estimate the distance from Melbourne Airport to the Melbourne CBD correct to the nearest 10 \text{ km}.

b

If a taxi charges \$1.80 per kilometre in addition to a \$3 booking fee and \$5 for road tolls, estimate a fare into town in dollars.

c

If the car travels at an average of 60\text{ km/h}, how long will the trip take in minutes?

8

Consider the following map:

a

Given the scale on the map, estimate the distance from Southbank helipad to Geelong correct to the nearest 10 \text{ km}.

b

A chartered helicopter travels at an average speed of 210\text{ km/h}. How many minutes should the flight last?

c

The helicopter cost \$10 per minute plus a booking fee of \$60. Estimate the cost of the chartered flight

9

Aashish wanted to travel from Auckland to Wellington. However, he could not drive the entire distance in one go. He decided to make one stop on the way at a hotel in Taupo.

a

It took Aashish 5.4 hours to reach the hotel. If the distance between Auckland and Taupo is 3 \text{ cm} on the map, what was his average speed for the first part of the trip? Round your answer to one decimal place.

b

Aashish's average speed on the second trip was 53.8\text{ km/h}. If the trip took him 8 hours, what is the distance between Taupo and Wellington?

c

How far should the distance between Taupo and Wellington appear on the map? Round your answer to one decimal place.

d

The room at the hotel cost \$80. If the fuel cost is 158 cents/litre, and Aashish's car fuel usage is 7 kilometre/litre, what was the cost of the entire trip from Auckland to Wellington?

10

A taxi company wants to find the cost of a direct trip from Birkdale to Albany Creek to publish the fee for customers.

a

If the route distance between Birkdale and Albany Creek appears to be 8 \text{ cm} on the map, what is the actual route distance?

b

If the taxi's average speed for the trip is 22\text{ km/h}, how many hours does the trip take? Round your answer to one decimal place.

c

The taxi driver is paid \$22.82 per hour. The car's fuel usage is 8\text{ km/L} and the fuel cost is 147\text{c/L}. What is the total cost of the trip?

d

If the taxi company wants to publish the fee of the trip for 230\% of its total cost, How much would the customer have to pay?

11

A bus company is working out the cost of tickets based on \$0.31 per kilometre travelled.

a

The following table displays the distances between Huntleys Point and the rest of the areas as they appear on the map. Complete the table below:

\text{Area}\text{Distance on map (units)}\text{Actual distance (km)}
\text{Wolli Creek}8
\text{Kogarah}9.5
\text{Randwick}6.5
\text{Maroubra}11.5
b

If a customer is at a station in Huntleys Point and has only \$5.45 in his pockets, which areas can he reach?

12

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

a

Carl's first plane from Perth to Sydney took 4 hours of flight time. If the airplane was travelling at an average speed of 825\text{ km/h}, estimate the distance between Perth and Sydney.

b

How many scaled units of 500\text{ km} should fit on the map between Perth and Sydney?

c

If the distance between Sydney and Adelaide appears to be 2.2 scaled units on the map, estimate the distance between Sydney and Adelaide.

d

Carl's second trip took 2.2 hours. Find the average speed of the airplane during the flight from Sydney to Adelaide.

e

Estimate the total distance Carl travelled during the flights.

f

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

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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

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