Contents

Introduction

Solving Simple Equations

Formulae

Factorising Quadratic Equations

Completing the Square method

General Solution method

Problem Solving

Quiz 

Algebra Main Page

Problem Solving involving Quadratic Equation

Example 1

A small swimming pool can be filled by two pipes in 3 hours. If the larger pipe alone takes 8 hours less than the smaller pipe to fill the pool, find the time in which it will be filled by each pipe singly.

Let the time taken by smaller pipe to fill the pool be x h.

In 1h, it can fill 1/x of the pool.

Let x - 8 be the time taken by larger pipe. 

In 1h, it can fill 1/(x-8) of the pool.

In 1h, both pipes fill 1/3 of the pool.

larger pipe= 12h - 8h = 4h

The larger pipe takes 4h and the smaller pipe takes 12 h.  

Example 2

A group of students are a tour. The total fare is $120 and this is to be shared equally among the students. If two more students join the tour, each will pay $2 less. Find the original number of students in the group.

Let x be the original no. of students.

The original number is 10.

Example 3

The length and breadth of a rectangle are (x + 4) cm and x cm respectively. Write the expression (i) the perimeter of the rectangle and (ii) the length of the side of a square with the same perimeter.

If the sum of the areas of the square and the rectangle is 94cm²,find x.

i) Perimeter = 2(x + 4) + 2x

ii) Length =