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Alanna went for a run. She ran
d kilometers at an average speed of
v kilometers per hour, and then walked to cool down for 0.25 hours. The total duration of the trip was
t hours.
Write an equation that relates
d,v, and
t.

Alanna went for a run. She ran $d$ kilometers at an average speed of $v$ kilometers per hour, and then walked to cool down for $0$ . $25$ hours. The total duration of the trip was $t$ hours. $\newline$ Write an equation that relates $d, v$ , and $t$ .

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Write equations of cosine functions using properties

Full solution

Q. Alanna went for a run. She ran

d

kilometers at an average speed of

v

kilometers per hour, and then walked to cool down for

0

.

25

hours. The total duration of the trip was

t

hours.

\newline

Write an equation that relates

d, v

, and

t

.

Calculate Time Spent: Determine the time spent running. $\newline$ The time spent running can be calculated by dividing the distance by the average speed. $\newline$ Time spent running = $\frac{\text{Distance}}{\text{Average speed}}$
Express in Terms of $d$ and $v$ : Express the time spent running in terms of $d$ and $v$ . Using the formula from Step $1$ , we have: Time spent running = $\frac{d}{v}$
Account for Walking Time: Account for the time spent walking. $\newline$ Alanna walked to cool down for $0.25$ hours, which is a known duration and does not depend on $d$ or $v$ . $\newline$ Time spent walking = $0.25$ hours
Write Total Duration Equation: Write the equation for the total duration of the trip. $\newline$ The total duration of the trip $t$ is the sum of the time spent running and the time spent walking. $\newline$ Total duration $t$ = Time spent running + Time spent walking
Substitute Expressions: Substitute the expressions for time spent running and walking into the equation for total duration. $\newline$ Using the expressions from Steps $2$ and $3$ , we get: $\newline$ $t = \frac{d}{v} + 0.25$

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