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Wilmer went up the hill for
x minutes at a speed of
y kilometers per minute. Then he went down the same path at a speed of
z kilometers per minute, and it took
him w minutes to do it.
Write an equation that relates
x,y,
z, and
w.

Wilmer went up the hill for $x$ minutes at a speed of $y$ kilometers per minute. Then he went down the same path at a speed of $z$ kilometers per minute, and it took $\operatorname{him} w$ minutes to do it. $\newline$ Write an equation that relates $x, y$ , $z$ , and $w$ .

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Write and solve equations for proportional relationships

Full solution

Q. Wilmer went up the hill for

x

minutes at a speed of

y

kilometers per minute. Then he went down the same path at a speed of

z

kilometers per minute, and it took

\operatorname{him} w

minutes to do it.

\newline

Write an equation that relates

x, y

,

z

, and

w

.

Denoting the distance: Let's denote the distance of the hill as $D$ kilometers. When Wilmer goes up the hill, the distance he covers is the product of the time spent going up and his speed going up. So, the distance $D$ can be expressed as: $\newline$ $D = x \times y$
Distance going up the hill: Similarly, when Wilmer goes down the hill, the distance he covers is the product of the time spent going down and his speed going down. So, the distance $D$ can also be expressed as: $\newline$ $D = w \times z$
Distance going down the hill: Since the distance going up the hill and down the hill is the same, we can set the two expressions for $D$ equal to each other: $\newline$ $x \cdot y = w \cdot z$
Equating the distances: Now we have an equation that relates $x$ , $y$ , $z$ , and $w$ :
$x \cdot y = w \cdot z$
This is the equation that shows the relationship between the time and speed going up and down the hill.

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