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1.04 Modelling using simultaneous equations

Interactive practice questions

A cat moves down a path at $8$8 m/s. A dog begins moving down the same path from the same point at a speed of $12$12 m/s, but starts $2$2 seconds later.

a

Which of the following graphs correctly depicts the distance travelled by each animal, measuring the time from when the cat starts running?

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A

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B

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C

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D
b

How long will it be before the dog catches up with the cat?

c

How far from the initial point will this be?

Easy
1min

A family owns two businesses, EcoLine and Helios. These businesses made a combined profit of $\$12$$12 million in the previous financial year, with Helios making $3$3 times as much profit as EcoLine.

Let $x$x represent the profit (in millions of dollars) of EcoLine, and $y$y be the profit (in millions of dollars) of Helios.

Easy
6min

A rectangular zone is to be $2$2 cm longer than it is wide, with a total perimeter of $20$20 cm.

Easy
5min

A mother is currently $6$6 times her son's age. In $4$4 years time, she will be $4$4 times her son's age.

Let $x$x and $y$y be the present ages of the son and mother respectively.

Easy
5min
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Outcomes

MS2-12-1

uses detailed algebraic and graphical techniques to critically evaluate and construct arguments in a range of familiar and unfamiliar contexts

MS2-12-6

solves problems by representing the relationships between changing quantities in algebraic and graphical forms

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