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IP1 Class Test (May 2025) Q13

IP1 Class Test (May 2025) Q13

IP 1
8 marks
  1. A train is travelling at a constant speed of \(x\) km/h for \(40\) km. Then it slows down and travels \(\left(25 + \frac{x}{5}\right)\) km at a constant speed of \(15\) km/h slower. Given that it takes \(12\) minutes shorter to travel the first \(40\) km, form an equation and show that it reduces down to \(\frac{200 + x}{5x} = \frac{125 + x}{5x - 75}\).[2]
  2. Solve the equation in (i). Hence, or otherwise, find the average speed of the train for the whole journey.[4]
  3. After the train slows down, it takes \(72\) seconds to pass a lamp post. Find the length of the train.[2]

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Answer:(i) \(\dfrac{200+x}{5x}=\dfrac{125+x}{5x-75}\) (ii) \(x=50\text{ km/h}\), average speed \(=\dfrac{125}{3}\text{ km/h}\approx41.7\text{ km/h}\) (iii) \(700\text{ m}\)

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