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.

Question

How many hours will it take for Amelia and Colette to have made the same number of flowers?
Simplify any fractions.
hours

Answer 1

Let \( t \) be the number of hours that Colette has been making flowers.

Amelia has already made 12 flowers and makes 10 more flowers each hour, so the total number of flowers Amelia has made after \( t \) hours is:

\[ 12 + 10t \]

Colette starts from zero and makes 14 flowers each hour, so the total number of flowers Colette has made after \( t \) hours is:

\[ 14t \]

We want to find the time \( t \) when both Amelia and Colette have made the same number of flowers. This gives us the equation:

\[ 12 + 10t = 14t \]

Now, we can solve for \( t \):

1. Subtract \( 10t \) from both sides:

\[ 12 = 14t - 10t \] \[ 12 = 4t \]

2. Divide both sides by 4:

\[ t = \frac{12}{4} = 3 \]

Thus, it will take \( \boxed{3} \) hours for Amelia and Colette to have made the same number of flowers.

To confirm, we can check the number of flowers each will have made after 3 hours:

• Amelia's flowers: \[ 12 + 10 \cdot 3 = 12 + 30 = 42 \]

• Colette's flowers: \[ 14 \cdot 3 = 42 \]

Both will have made 42 flowers after 3 hours. Therefore, the solution is verified, and the answer is indeed \( \boxed{3} \).