Use the table to answer the question

Question

Time ( hrs ) 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?

( 2, 60 )

( 15, 1/2 )

( 1 1/2, 30 )

( 1, 30 )

Answer 1

To determine the ratio that represents the constant of proportionality from the provided data, we can analyze any of the pairs in the table, as they should yield the same ratio if proportionality is consistent.

The constant of proportionality (k) can be determined using the formula:

\( k = \frac{\text{Pages read}}{\text{Time (hrs)}} \)

We can calculate k for each pair:

1. For (1/2, 15): \[ k = \frac{15}{1/2} = 15 \times 2 = 30 \]

2. For (1, 30): \[ k = \frac{30}{1} = 30 \]

3. For (1 1/2, 45): \[ k = \frac{45}{1.5} = 30 \]

4. For (2, 60): \[ k = \frac{60}{2} = 30 \]

All calculations yield a proportionality constant \( k = 30 \).

Thus, we can select any of the provided points that maintain this consistency. The options for a ratio are given as:

• (2, 60)
• (15, 1/2)
• (1 1/2, 30)
• (1, 30)

Considering we want to maintain the same constant of proportionality (k = 30), we can use (2, 60) which directly represents the relationship where the constant of proportionality is maintained because:

\[ \frac{60}{2} = 30 \]

Hence, the ratio indicating the constant of proportionality is:

(2, 60)