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A circular field has a circumference of $240\,\text{km}$ , $3$ cyclists start together 1 can cycle $30$ , $40 ,48\,\text{km}$ a day. Round the fields when will they meet again.

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Weighted averages: word problems

Full solution

Q. A circular field has a circumference of

240\,\text{km}

,

3

cyclists start together 1 can cycle

30

,

40 ,48\,\text{km}

a day. Round the fields when will they meet again.

Calculate Time for Each Cyclist: Calculate the time it takes for each cyclist to complete one lap around the field. $\newline$ - Cyclist A: $240 \, \text{km} / 30 \, \text{km/day} = 8 \, \text{days}$ $\newline$ - Cyclist B: $240 \, \text{km} / 40 \, \text{km/day} = 6 \, \text{days}$ $\newline$ - Cyclist C: $240 \, \text{km} / 48 \, \text{km/day} = 5 \, \text{days}$
Determine Least Common Multiple: Determine the least common multiple (LCM) of the times to find when all cyclists will meet. $\newline$ - LCM of $8$ , $6$ , and $5$ is $120$ days.

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