Year 10 Interactive Maths - Second Edition

## Problem Solving

Quadratic equations are often used to solve problems in science or in the design of objects to be constructed. Many word problems involve:
• distance, speed and time
• area of a paddock or path
• projectiles
• construction of bridges
• logos

The following approach may be useful to solve and model word problems.

• Draw a diagram if necessary and let the unknown quantity be x or some other suitable pronumeral.
• Using the given information, write an equation in terms of x and solve it.
• Check the reasonableness of the solution and state the answer in words.

#### Example 11

A cyclist takes (x + 3) hours to travel a distance of 108 kilometres when cycling at x kilometres per hour. Find:
a.  the value of x
b.  the time take to complete the journey

#### Example 12

A swimming pool 17 m by 15 m is surrounded by a concrete path, as shown in the following diagram.

#### Example 13

##### Solution:

Multiply both sides by 2

So, the width of the base is 3 cm.

#### Example 14

The number of square metres in a square room's floor area exceeds the number of metres in the room's perimeter by 60. Find the side-length of the room.