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3.02 Compare rates

Worksheet
Unit price
1

For each of the following determine the price of one unit:

a

Three apples cost \$3.63

b

Twelve eggs cost \$3.84

c

Four pies cost \$21.00

d

Five hotdogs cost \$12.00

2

Consider the following sales:

  • 6 pencil cases for \$24 at Big Z.
  • 9 pencil cases for \$54 at X-mart.
a

What is the cost of a single pencil case at Big Z?

b

What is the cost of a single pencil case at X-mart?

c

Hence which is the best place to buy pencil cases, if you want the best price per item?

3

Consider the following prices of mangos:

  • 148 mangos for \$384.80 at shop A, or

  • 252 mangos for \$453.60 at shop B

a

What is the cost of a single mango at shop A?

b

What is the cost of a single mango at shop B?

c

Hence, which is the best place to buy mangos, if you want the best price per item?

Compare rates
4

Avril is running from John in a game of tag. Avril runs 30 \text{ m} every 5 \text{ sec} and John runs 21 \text{ m} every 3 \text{ sec}.

a

Calculate:

i

Avril's speed in metres per second.

ii

John's speed in metres per second.

b

Who is faster? Avril or John?

5

2 shearers wanted to work out who was the faster shearer. Jenny sheared 144 sheep over 6 days, and Sean sheared 115 sheep in 5 days.

a

Calculate:

i

Jenny's rate in sheep per day.

ii

Sean's rate in sheep per day.

b

If Jenny continued at this rate, how many sheep would she be able to shear in 25 days?

c

Who sheared sheep at a faster daily rate? Sean or Jenny?

6

Movie World theme park on the Gold Coast had 2325 visitors enter over the course of 7.5 hours on Wednesday. On Friday, it had 2050 visitors enter over a 5-hour period.

If there are more than 380 people entering the park per hour, then Movie World adds extra staff at the gate.

a

State the rate at which visitors were entering the park per hour on Wednesday.

b

State the rate at which visitors were entering the park per hour on Friday.

c

On which day were extra staff required?

7

Neville is deciding between 4 cars to buy. He wants to buy the most fuel efficient one.

a

Complete the table.

\text{Car}\text{Litres used}\text{Distance travelled (km)}\text{L/km}
\text{Magnum}13.40538.3
\text{Falcador}20.7154.5
\text{Canyonero}6.33619.2
\text{Civil}2.7548.1
b

Which car is the most fuel efficient?

c

Fuel consumption is usually given in \text{L/} 100 \text{ km}. Convert the fuel consumption rate for the Magnum to this rate.

8

A car travels 80 \text{ km} and consumes 6.96 \text{ L} of fuel.

a

Find the rate of fuel consumption of the car in \text{ L/km}. Round your answer to three decimal places.

b

State the rate of fuel consumption of the car in \text{L/} 100 \text{ km}.

9

Find the rate of fuel consumption for each car in \text{L/} 100 \text{ km}:

a

A car travels 50 \text{ km} and consumes 7 \text{ L} of fuel.

b

Fiona's car can travel 12\,500 \text{ km} on 504 \text{ L} of fuel.

10

Tom's car can travel 5000 \text{ km} on 1260 \text{ L} of fuel. Susana's car can travel 1600 \text{ km} on 192 \text{ L} of fuel.

a

Find the rate of fuel consumption of:

i

Tom's car in \text{L/} 100 \text{ km}

ii

Susana's car in \text{L/} 100 \text{ km}

b

Who has the most fuel efficient car?

11

Christa and Ben each own a car, but they decide to carpool together to save money. They want to figure out whose car will be cheaper to run.

Christa's car has a rate of fuel consumption of 5 \text{ L/} 100 \text{ km}. Ben's car has a fuel economy of 35 \text{ km/L}.

a

Calculate the fuel economy of Christa's car in \text{km/L}. Round your answer to the nearest whole number.

b

Whose car should they take to save fuel?

12

John and Tracy each own a car, but they decide to carpool together to save money. They want to figure out whose car will be cheaper to run.

John's car has a rate of fuel consumption of 5.8 \text{ L/} 100 \text{ km}. Tracy's car has a fuel economy of 16 \text{ km/L}.

a

Calculate the fuel economy of John's car in \text{km/L}, to two decimal places.

b

Whose car should they take to save fuel?

13

Determine whether each girl's car is more efficient or less efficient than the reported car fuel consumption:

a

A make of car is reported to have a rate of fuel consumption of 6.6 \text{ L/}100 \text{ km}. Sharon has this make of car and has calculated the rate of her fuel consumption to be 0.186 \text{ L/km}.

b

A make of car is reported to have a rate of fuel consumption of 7.1 \text{ L/} 100 \text{ km}. Skye has this make of car and has calculated the rate of her fuel consumption to be 0.041 \text{ L/km}.

14

A Wisconsin freight train travels 50 \text{ km/h} faster than the intercity passenger train. The Wisconsin freight train travels 600 \text{ km} in the same time that it takes the intercity passenger train to travel only 400 \text{ km}.

a

Express v, the speed of the Wisconsin freight train in terms of s, the speed of the intercity passenger train.

b

Express the travel time of the intercity passenger train in terms of s.

c

Express the travel time T of the Wisconsin freight train in terms of s.

d

Using parts (b) and (c), form an equation and hence determine the speed of the intercity passenger train.

e

Hence find v, the speed of the Wisconsin freight train.

15

Lachlan cycles at v \text{ km/hr} to San Diego while Ryan cycles at s \text{ km/hr} to Los Angeles in the same amount of time. Lachlan covers 48 \text{ km}, while Ryan covers 68 \text{ km}. Lachlan travels at a speed that is 5 \text{ km/h} slower than Ryan.

Find the speed at which Lachlan cycles.

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Outcomes

1.1.2.1

review identifying common usage of rates, including km/h

1.1.2.4

use rates to make comparisons

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