Question

Amelia and Colette are making tissue-paper flowers for a school dance. Amelia has already made 12 flowers, and she makes an additional 10 flowers each hour. Colette has just started, and she makes 14 flowers each hour.
How many hours will it take for Amelia and Colette to have made the same number of flowers?
Simplify any fractions.

Answer 1

To find out how many hours it will take for both Amelia and Colette to have made the same number of flowers, we can set up an equation.

Let \( h \) represent the number of hours that Colette has been working.

Amelia starts with 12 flowers and makes an additional 10 flowers each hour, so the total number of flowers she has after \( h \) hours is:
\[
12 + 10h
\]

Colette starts with 0 flowers and makes 14 flowers each hour, so the total number of flowers she has after \( h \) hours is:
\[
14h
\]

We want to find when both have made the same number of flowers. Thus, we set the equations equal to each other:
\[
12 + 10h = 14h
\]

Next, we can solve for \( h \):
1. Subtract \( 10h \) from both sides:
\[
12 = 14h - 10h
\]
\[
12 = 4h
\]

2. Divide both sides by 4:
\[
h = \frac{12}{4} = 3
\]

Therefore, it will take **3 hours** for Amelia and Colette to have made the same number of flowers.

To verify:
- After 3 hours, Amelia will have made:
\[
12 + 10 \times 3 = 12 + 30 = 42 \text{ flowers}
\]

- After 3 hours, Colette will have made:
\[
14 \times 3 = 42 \text{ flowers}
\]

Both Amelia and Colette will have made **42 flowers** after 3 hours, confirming that our solution is correct.

Thus, the final answer is:
\[
\boxed{3}
\]