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Circles, SM-Bank 038

Evan rides his bike around a circular track with a radius of 150 metres.

He rides the track 5 days a week and wants to have ridden 230 kilometres by the end of the week.

What is the minimum number of laps, to the nearest whole lap, he must complete each day to achieve his target?  (3 marks)

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\(49\ \text{laps}\)

Show Worked Solution

\(\text{Total Distance}=230\ \text{km}=230\ 000\ \text{m}\)

\(\text{Total laps}\) \(=\dfrac{230\ 000}{C}\)
  \(=\dfrac{230\ 000}{300\pi}\)
  \(=244.037\dots\)

 

\(\text{Laps per day:}\) \(=\dfrac{244.037\dots}{5}\)
  \(=48.807\dots\)
  \(\approx 49\ \text{laps}\)

 
\(\therefore\ \text{Evan needs to ride }49\ \text{laps per day to achieve his goal}.\)

\(\Big[\text{Check:  }49\times 5\times 300\pi=230\ 907.06\ \text{m}=230.907\ \text{km}\Big]\)