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Fen completed a triathlon race whose total distance is
D kilometers. First, she swam a distance of 0.5 kilometer. Then, she rode a bicycle for
x hours at an average speed of 20 kilometers per hour. Finally, she ran for 0.5 hour at an average speed of
v kilometers per hour.
Write an equation that relates
D,
x, and
v.

Fen completed a triathlon race whose total distance is $D$ kilometers. First, she swam a distance of $0$ . $5$ kilometer. Then, she rode a bicycle for $x$ hours at an average speed of $20$ kilometers per hour. Finally, she ran for $0$ . $5$ hour at an average speed of $v$ kilometers per hour. $\newline$ Write an equation that relates $D$ , $x$ , and $v$ .

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Write and solve equations for proportional relationships

Full solution

Q. Fen completed a triathlon race whose total distance is

D

kilometers. First, she swam a distance of

0

.

5

kilometer. Then, she rode a bicycle for

x

hours at an average speed of

20

kilometers per hour. Finally, she ran for

0

.

5

hour at an average speed of

v

kilometers per hour.

\newline

Write an equation that relates

D

,

x

, and

v

.

Identify Distances: Identify the distances covered in each part of the triathlon. The total distance $D$ is the sum of the distances covered by swimming, biking, and running.
Calculate Swimming Distance: Calculate the distance covered by swimming. $\newline$ Fen swam a distance of $0.5$ kilometer. $\newline$ $\text{Distance\_swimming} = 0.5 \, \text{km}$
Calculate Biking Distance: Calculate the distance covered by biking. $\newline$ Fen biked for $x$ hours at an average speed of $20$ kilometers per hour. $\newline$ $\text{Distance}_{\text{biking}} = \text{Speed}_{\text{biking}} \times \text{Time}_{\text{biking}}$ $\newline$ $\text{Distance}_{\text{biking}} = 20 \, \text{km/h} \times x \, \text{h}$ $\newline$ $\text{Distance}_{\text{biking}} = 20x \, \text{km}$
Calculate Running Distance: Calculate the distance covered by running. $\newline$ Fen ran for $0.5$ hour at an average speed of $v$ kilometers per hour. $\newline$ $\text{Distance\_running} = \text{Speed\_running} \times \text{Time\_running}$ $\newline$ $\text{Distance\_running} = v \, \text{km/h} \times 0.5 \, \text{h}$ $\newline$ $\text{Distance\_running} = 0.5v \, \text{km}$
Combine Distances for Total Distance: Combine the distances to form the equation for the total distance $D$ . $D = \text{Distance\_swimming} + \text{Distance\_biking} + \text{Distance\_running}$ $D = 0.5 + 20x + 0.5v$

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