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Solving quadratic equations sheet
5-mark answer frame

A bus covers a 300 km journey at a uniform speed. If its speed were 10 km/h more, the journey would take 1 hour less. Find its speed.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Distance 300 km; 10 km/h more saves 1 hour. To find: the speed.
  2. 2 · Choose the unknown and write the formula. Let the speed be x km/h. Time = distance ÷ speed.
  3. 3 · Form the equation from the story. 300/x − 300/(x + 10) = 1, which gives x² + 10x − 3000 = 0.
  4. 4 · Solve. (x + 60)(x − 50) = 0, so x = 50 or x = −60.
  5. 5 · Reject the impossible root. A speed cannot be negative, so x = 50.
  6. 6 · Check and box the answer. 300/50 = 6 h and 300/60 = 5 h, so 1 hour less. Box: speed = 50 km/h.

Scoring tip: Begin with 'Let the speed be x km/h'. Rejecting the negative root with a reason earns a mark.