Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $w$ .

View step-by-step help

View step-by-step help

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.

More problems from Write and solve equations for proportional relationships

Question

Read the description of a proportional relationship. Every spring, Kenny plants colorful flowers in his garden. This year, he decides to plant petunias. He buys them at the garden store, brings them back home, and starts planting. There is a proportional relationship between the amount of time (in minutes) Kenny has been working in his garden,

x

, and the number of petunias he has planted,

y

. After working in his garden for

2

minutes, Kenny has planted

4

petunias. Write the equation for the relationship between

x

y

y = \_\_\_

Posted 2 months ago

Question

Addison painted her room. She had

50

square meters to paint, and she painted at a constant rate. After

2

hours of painting, she had

35

square meters left.

\newline

y

represent the area (in square meters) left to paint after

x

\newline

Complete the equation for the relationship between the area and number of hours.

\newline

y=

Posted 4 months ago

Question

V=\ell w h

\newline

The formula gives the volume

V

of a right rectangular prism with length

\ell

w

h

. What is the volume, in cubic meters, of a rectangular prism that is

6

2

meters wide, and

10

Posted 4 months ago

Question

A certain factory produces and sells

x

kilograms of ice cream per month. It costs

c

dollars to produce one kilogram of ice cream, which is then sold for

\mathbf{0 . 1 6}

dollars. The factory's monthly net profit is

P

\newline

Write an equation that relates

x, c

P

Posted 1 month ago

Question

x

delivery persons carry a total of

B

bags of groceries up the stairs. They can each carry

y

bags at a time, and they each make

2

trips up the stairs.

\newline

Write an equation that relates

x

B

y

Posted 2 months ago

Question

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

v

Posted 2 months ago

Question

A baker needs more than

120

minutes to let their dough rise.

\newline

Write an inequality that describes

m

, the number of minutes needed for the dough to rise.

Posted 1 month ago

Question

Ha-yoon can dive to a depth of

7

meters. Ji-woo cannot dive as deep as

\mathrm{Ha}

\newline

Write an inequality that describes

j

, the depths Ji-woo can dive to in meters.

Posted 1 month ago

Question

Richard and Jordan went to see a movie. Richard spent

m

dollars at the movie theater, and Jordan spent

\$ 12

at the movie theater. Together they spent a total of

\$ 26

\newline

Write an equation to describe this situation.

Posted 3 months ago

Question

Isabel tried to evaluate an expression step by step.

(2+8)+8

. Find Isabel's first mistake

Posted 13 hours ago