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Xóchitl, who has already warmed up, immediately starts to pedal at a rate of
18(km)/(h) on a stationary bike.
She sees that her friend Cowessess has already pedaled. 12 minutes at an average rate of
10(km)/(h).
Assuming Cowessess's rate stays the same, how long would Xóchitl have to pedal to catch up to Cowessess's distance?

Xóchitl, who has already warmed up, immediately starts to pedal at a rate of $18 \frac{\mathrm{km}}{\mathrm{h}}$ on a stationary bike. $\newline$ She sees that her friend Cowessess has already pedaled. $12$ minutes at an average rate of $10 \frac{\mathrm{km}}{\mathrm{h}}$ . $\newline$ Assuming Cowessess's rate stays the same, how long would Xóchitl have to pedal to catch up to Cowessess's distance?

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Solve proportions: word problems

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Q. Xóchitl, who has already warmed up, immediately starts to pedal at a rate of

18 \frac{\mathrm{km}}{\mathrm{h}}

on a stationary bike.

\newline

She sees that her friend Cowessess has already pedaled.

12

minutes at an average rate of

10 \frac{\mathrm{km}}{\mathrm{h}}

.

\newline

Assuming Cowessess's rate stays the same, how long would Xóchitl have to pedal to catch up to Cowessess's distance?

Calculate Distance Covered: Calculate the distance Cowessess has already covered. $\newline$ Cowessess has pedaled for $12$ minutes at a rate of $10\,\text{km/h}$ . To find the distance, we convert the time to hours and multiply by the rate. $\newline$ $12$ minutes $= \frac{12}{60}$ hours $= 0.2$ hours $\newline$ Distance $=$ Rate $\times$ Time $\newline$ Distance $= 10\,\text{km/h} \times 0.2\,\text{hours}$ $\newline$ Distance $= 2\,\text{km}$
Determine Time for Xóchitl: Determine how long it will take Xóchitl to cover the same distance. $\newline$ Xóchitl is pedaling at a rate of $18 \, \text{km/h}$ . To find the time it takes to cover $2 \, \text{km}$ , we divide the distance by Xóchitl's rate. $\newline$ Time = Distance / Rate $\newline$ Time = $2 \, \text{km} / 18 \, \text{km/h}$ $\newline$ Time = $1/9 \, \text{hours}$ $\newline$ To convert this time into minutes, we multiply by $60$ . $\newline$ Time in minutes = $(1/9) \times 60$ $\newline$ Time in minutes = $6.666\ldots$ minutes $\newline$ Xóchitl would need to pedal for approximately $6.67$ minutes to cover $2 \, \text{km}$ .

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