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.
Which of the following graphs correctly depicts the distance travelled by each animal, measuring the time from when the cat starts running?
How long will it be before the dog catches up with the cat?
How far from the initial point will this be?
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.
A rectangular zone is to be $2$2 cm longer than it is wide, with a total perimeter of $20$20 cm.
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.