Questions: The relationship between the time in minutes and pieces of bamboo eaten is proportional. Ling ling, the panda, can eat 6 pieces of bamboo in 4 minutes. Find the constant of proportionality.

Solution Steps

The relationship between time \( x \) (in minutes) and pieces of bamboo \( y \) is proportional. This means: \[ y = kx \] where \( k \) is the constant of proportionality.

Given that Ling Ling eats 6 pieces of bamboo in 4 minutes, we can substitute \( x = 4 \) and \( y = 6 \) into the equation: \[ 6 = k \cdot 4 \] Solving for \( k \): \[ k = \frac{6}{4} = 1.5 \] The constant of proportionality is \( k = 1.5 \).

Using the equation \( y = 1.5x \), we can calculate the missing values in the table:

1. For \( x = 0 \): \[ y = 1.5 \cdot 0 = 0 \]
2. For \( x = 1 \): \[ y = 1.5 \cdot 1 = 1.5 \]
3. For \( x = 2 \): \[ y = 1.5 \cdot 2 = 3 \]
4. For \( x = 3 \): \[ y = 1.5 \cdot 3 = 4.5 \]
5. For \( x = 4 \): \[ y = 1.5 \cdot 4 = 6 \]

The completed table is:

\[ \begin{tabular}{|c|c|} \hline Time in Minutes, \( x \) & Pieces of Bamboo, \( y \) \\ \hline 0 & 0 \\ \hline 1 & 1.5 \\ \hline 2 & 3 \\ \hline 3 & 4.5 \\ \hline 4 & 6 \\ \hline \end{tabular} \]

Final Answer