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Justin runs at a constant rate, traveling
17km in 2 hours.
Write an equation that shows the relationship between
d, the distance he runs in kilometers, and
h, the time he spends running in hours.
Do NOT use a mixed number.

Justin runs at a constant rate, traveling $17 \mathrm{~km}$ in $2$ hours. $\newline$ Write an equation that shows the relationship between $d$ , the distance he runs in kilometers, and $h$ , the time he spends running in hours. $\newline$ Do NOT use a mixed number.

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Write linear functions: word problems

Full solution

Q. Justin runs at a constant rate, traveling

17 \mathrm{~km}

in

2

hours.

\newline

Write an equation that shows the relationship between

d

, the distance he runs in kilometers, and

h

, the time he spends running in hours.

\newline

Do NOT use a mixed number.

Determine Running Rate: Determine Justin's running rate. $\newline$ Justin runs $17 \, \text{km}$ in $2 \, \text{hours}$ . To find his running rate, we divide the distance by the time. $\newline$ Rate $=$ Distance $/$ Time $\newline$ Rate $=$ $17 \, \text{km}$ $/$ $2 \, \text{hours}$
Calculate Rate: Calculate the running rate. $\newline$ Now we perform the division to find the rate. $\newline$ Rate = $\frac{17 \, \text{km}}{2 \, \text{hours}} = 8.5 \, \text{km/hour}$
Write Equation: Write the equation for the relationship between distance and time. $\newline$ Since the rate is constant, the distance Justin runs is directly proportional to the time he spends running. The equation that represents this relationship is: $\newline$ $d = \text{Rate} \times h$
Substitute Rate: Substitute the calculated rate into the equation. $\newline$ We know the rate is $8.5 \, \text{km/hour}$ , so we substitute this value into the equation. $\newline$ $d = 8.5 \times h$
Ensure Correct Form: Ensure the equation does not use a mixed number. The rate is already expressed as a decimal, not a mixed number, so the equation is in the correct form.

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