## Cycling distance calculations

 Difficulty: Rating: GCSE Marks:

GCSE Text:
Raj has ridden his bicycle all weekend, and the tracking app on his phone tells him that the wheel has rotated 13,725 times in that time.  If the bike’s wheel diameter is 26″, how far has Raj ridden in km this weekend?

Suggestions:
A complex question which needs students to have an understanding of circle formulae, conversion of distances (imperial to metric) and the ability to convert cm to metres and km.  It is important to stress to students that given the high marks awarded for a question of this type, even if the overall method proves too difficult for them, method marks will be awarded for working out any of the following:

• Use of correct circumference formula with numbers substituted
• Correct circumference of the wheel in inches
• Correct conversion from inches to a metric unit

Extension Ideas:
Teachers could extend the learning by considering:

• Raj’s friend Bo has just bought a new bike with 29″ wheels. If Bo has ridden the same distance as Raj, how many times has his wheel rotated?