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RSS 2EM EOY P2 2023 Q12

RSS 2EM EOY P2 2023 Q12

Secondary 2
8 marks

Victor cycles at a speed of \(x\) km/h up a \(30\) km slope.

  1. Write down, in terms of \(x\), the number of hours he took to cycle up the slope.[1]

He then cycles at a speed of \((x + 5)\) km/h down the same slope.

  1. Write down, in terms of \(x\), the number of hours he took to cycle down the slope.[1]
  2. The difference in time taken is \(18\) minutes.
    Write down an equation in \(x\) to represent this information and show that it reduces to
    \(x^2 + 5x - 500 = 0.\)[2]
  3. Solve the equation \(x^2 + 5x - 500 = 0\).[2]
  4. Hence, calculate the total time taken, in hours and minutes, Victor took for the whole journey.

Solution:

Solution locked

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Answer:(a) \(\dfrac{30}{x}\text{ h}\) (b) \(\dfrac{30}{x+5}\text{ h}\) (c) \(\dfrac{30}{x}-\dfrac{30}{x+5}=\dfrac3{10}\Rightarrow x^2+5x-500=0\) (d) \(x=-25\) or \(x=20\) (e) \(2\text{ h}\hspace{0.5em}42\text{ min}\)

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