Cycling and walking time model

Cycling and walking time model

Secondary 2
10 marks
TGM Original Questions

Optional extension

A cyclist rides \(40\) km at \(x\) km/h before a breakdown, then walks \(8\) km at \((x-16)\) km/h. The whole trip takes \(4\) hours.

  1. Write the cycling time.[2]
  2. Write the walking time.[2]
  3. Form an equation and show that \(x^2-28x+160=0\).[2]
  4. Solve and reject the invalid root.[2]
  5. Find, in hours and minutes, the time for all \(48\) km if completed at the original cycling speed.[2]

Solution:

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Answer:(a) \(\dfrac{40}{x}\) h (b) \(\dfrac8{x-16}\) h (d) \(x=20\) km/h (e) \(2\) h \(24\) min. (c) \(x^2-28x+160=0\) (shown).

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