Question

Caden and his little sister, Nina, went blackberry picking. Caden helped Nina get started until she had 42 berries. When Caden started picking his own berries, he picked 11 berries per minute while Nina continued to pick 5 berries per minute.
Which equation can you use to find m, the number of minutes it took for Caden to have as many berries as Nina?
After how many minutes did Caden have as many berries as Nina?
Simplify any fractions.
minutes

Answer 1

Let's define the quantities involved:

- At the beginning, Nina has 42 berries.
- Caden picks berries at a rate of 11 berries per minute.
- Nina continues to pick berries at a rate of 5 berries per minute.

Let \( m \) be the number of minutes it takes for Caden to have as many berries as Nina.

After \( m \) minutes, the number of berries Caden has can be expressed as:
\[ \text{Caden's berries} = 0 + 11m = 11m \]
(Caden starts with 0 berries)

Nina's total after \( m \) minutes will be:
\[ \text{Nina's berries} = 42 + 5m \]

We need to find the time \( m \) when Caden's berries are equal to Nina's berries:
\[ 11m = 42 + 5m \]

Now, let's solve for \( m \).
1. Subtract \( 5m \) from both sides:
\[ 11m - 5m = 42 \]
2. This simplifies to:
\[ 6m = 42 \]
3. Now divide both sides by 6:
\[ m = \frac{42}{6} = 7 \]

Thus, Caden will have as many berries as Nina after **7 minutes**.