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Three relnners cover a distance of
80cm.85cm and
90cm in every step. Find the least distance which will be covered by each runner in whole steps. Also, find the number of whole steps taken by each runner.

Three runners cover a distance of $80 \mathrm{~cm} ,85 \mathrm{~cm}$ and $90 \mathrm{~cm}$ in every step. Find the least distance which will be covered by each runner in whole steps. Also, find the number of whole steps taken by each runner.

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Evaluate variable expressions: word problems

Full solution

Q. Three runners cover a distance of

80 \mathrm{~cm} ,85 \mathrm{~cm}

and

90 \mathrm{~cm}

in every step. Find the least distance which will be covered by each runner in whole steps. Also, find the number of whole steps taken by each runner.

Identify Distances: Step $1$ : Identify the distances covered by each runner in one step. $\newline$ The distances are $80\,\text{cm}$ , $85\,\text{cm}$ , and $90\,\text{cm}$ .
Calculate LCM: Step $2$ : Calculate the LCM of $80$ , $85$ , and $90$ . First, find the prime factors: $80 = 2^4 \times 5$ , $85 = 5 \times 17$ , $90 = 2 \times 3^2 \times 5$ . LCM = $2^4 \times 3^2 \times 5 \times 17 = 12240$ cm.
Determine Number of Steps: Step $3$ : Determine the number of whole steps each runner takes to cover the LCM distance. $\newline$ For the first runner ( $80$ cm per step): $12240 \div 80 = 153$ steps. $\newline$ For the second runner ( $85$ cm per step): $12240 \div 85 = 144$ steps. $\newline$ For the third runner ( $90$ cm per step): $12240 \div 90 = 136$ steps.

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