Use the table to answer the question.

Question

Time (hours) Pages read
1/2 15
1 30
1 1 2 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?

Answer 1

To find the ratio of the constant of proportionality, we need to find the ratio between the number of pages read and the time in hours.

The ratio is calculated by dividing the pages read by the time in hours.

For the first row, the ratio is 15 pages / 0.5 hours = 30 pages/hour.

For the second row, the ratio is 30 pages / 1 hour = 30 pages/hour.

For the third row, the ratio is 45 pages / 1.5 hours = 30 pages/hour.

For the fourth row, the ratio is 60 pages / 2 hours = 30 pages/hour.

Therefore, the constant of proportionality is 30 pages per hour.

Answer 2

Use the table to answer the question.

Time (min) 1 2 3 7 10
Water Used (gal) 5 10 15 35 50
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.

Answer 3

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the two quantities remains constant.

We can do this by calculating the ratios for each row in the table.

For the first row, the ratio is 5 gallons / 1 minute = 5 gallons/minute.

For the second row, the ratio is 10 gallons / 2 minutes = 5 gallons/minute.

For the third row, the ratio is 15 gallons / 3 minutes = 5 gallons/minute.

For the fourth row, the ratio is 35 gallons / 7 minutes = 5 gallons/minute.

For the fifth row, the ratio is 50 gallons / 10 minutes = 5 gallons/minute.

Since the ratio between the water used and time in minutes remains constant (5 gallons/minute), the quantities in the data table are in a proportional relationship.

We can conclude that the amount of water used is directly proportional to the time in minutes.