7.1.9Solving Problems about Proportional Relationships

Multiple Choice

Diego runs at a constant rate. This means the time it takes for him to run a particular distance is proportional. The constant rate is also the constant of proportionality.

Remember that in a proportional relationship, the values for the first quantity are each multiplied by the constant of proportionality to get the values for the second quantity.

What number can you multiply by 5 to get 14? 

If it takes the runner 14 minutes to run 5 laps, how long does it take the runner to run 1 lap?

• 3 minutes

• 2.8 minutes

• 3.2 minutes

• 1.4 minutes

​The time Diego takes to complete one lap is the constant of proportionality of this scenario.

However, there is still one more piece of information you need to know to determine the time it would take him to finish the race. You have to know the distance or length of the race.

Poll

In Diego's training scenario in order to calculate how long a marathon would take, his pace needed to be calculated and then used with the distance of the race.

Reading and interpreting the given information carefully is an essential skill in mathematics.

What is pace?

• minutes per lap

• laps per minute

Match

Clare and Han ran different distances and marked their time in minutes for each set of laps. Match the following tables with the correct description.

This is a proportional relationship.

This relationship is not proportional.

This is Mrs. Vogt.

• This is a proportional relationship.

• This relationship is not proportional.

• This is Mrs. Vogt.

Multiple Choice

Gemelise timed how long it took a faucet to fill up different-sized containers. She created the table below.

Is the relationship between time in minutes and gallons of water proportional?

• Yes, it's proportional.

• No, it is not proportional.

Categorize

Options (7)

name of friends

where they are going

time: how long it took

distance: how far they went

constant rate: how fast they went

d = rt

1. Who will arrive at the park first?

Mai and Noah each leave their house at the same time and ride their bikes to the park.

1. For each person, write an equation that relates the distance they travel and the time.

2. Who will arrive at the park first?

given information

missing information

formula to use

question to be answered

Draw

Hint: Substitute Mai and Noah's rate for r in the equation d = rt.

You have enough information to write the equations. You still need more information to determine who reached the park first!

​Who will get to the park first, Mai or Noah?

• Mai and Noah each bike at a constant speed.

• Mai bikes 250 meters per minute and lives 8,000 meters from the park.

• Noah bikes 300 meters per minute and lives 9,000 meters from the park.

Multiple Choice

How long will it take Mai to bike 8000 meters at 250 meters per minute?

8,000 ÷ 250 = t

• t = 32 minutes

• t = 64 minutes

• t = 40 minutes

• t = 42 minutes

Multiple Choice

How long will it take Noah to bike 9,000 meters at 300 meters per minute?

9,000 ÷ 300 = t

• t = 31 minutes

• t = 30 minutes

• t = 300 minutes

• t = 3 minutes

Multiple Choice

Who will get to the park first, Mai or Noah?

• Mai

  8000/250 =32

• Noah

  9000/300 =30

​

​

Dropdown

A person worked for 150 minutes checking comments on a website for inappropriate content.

They were able to check 100 comments in 8 minutes.



How many comments are checked per minute? ​

Select answer

Multiple Choice

A person worked for 150 minutes checking comments on a website for inappropriate content. They were able to check 100 comments in 8 minutes.

How many comments are checked in 150 minutes?

• 1.5 comments

• 25 comments

• 1,875 comments

• 12.5 comments