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Algebraic Techniques, SM-Bank 101

Yesterday Gareth walked \(x\) kilometres in Kosciuszko National park.

He started at Thredbo village and walked up Merritts Nature Track to the Kosciuszko express chairlift. When he arrived at the chairlift he had complete \(\dfrac{1}{5}\) of the total distance.

Gareth then joined a walking group and walked a further \(\dfrac{1}{3}\) of the total distance before beginning his descent back to the village.

  1. Write an algebraic fraction to represent the distance he walked to the Kosciuszko express chairlift.  (1 mark)

  2. Write an algebraic fraction to represent the distance he walked with the walking group.  (1 mark)

  3. Using part (a) and (b) above, write a simplified algebraic fraction to represent the total distance Gareth covered in the first two legs of his walk.  (2 marks)

Show Answers Only

a.    \(\dfrac{x}{5}\ \text{kilometres}\)

b.    \(\dfrac{x}{3}\ \text{kilometres}\)

c.    \(\dfrac{8x}{15}\ \text{kilometres}\)

Show Worked Solution
a.    \(\text{First leg}\) \(=\dfrac{1}{5}\times x\)
    \(=\dfrac{x}{5}\ \text{kilometres}\)

 

b.    \(\text{Second leg}\) \(=\dfrac{1}{3}\times x\)
    \(=\dfrac{x}{3}\ \text{kilometres}\)

 

c.    \(\text{Distance travelled}\) \(=\dfrac{x}{5}+\dfrac{x}{3}\)
    \(=\dfrac{x}{5}\times \dfrac{3}{3}+\dfrac{x}{3}\times \dfrac{5}{5}\)
    \(=\dfrac{3x}{15}+\dfrac{5x}{15}\)
    \(=\dfrac{8x}{15}\ \text{kilometres}\)