Becky and her friend Eliana are knitting scarves for the homeless. Becky had already completed 12 scarves and has committed to making 1 more scarf per day. Eliana, who hasn't completed any scarves yet, has more free time and can make 4 scarves per day. At some point, Eliana will catch up and they will both have completed the same number of scarves. How many scarves will each woman have finished? How long will that take?

Question

Becky and her friend Eliana are knitting scarves for the homeless. Becky had already completed 12 scarves and has committed to making 1 more scarf per day. Eliana, who hasn't completed any scarves yet, has more free time and can make 4 scarves per day. At some point, Eliana will catch up and they will both have completed the same number of scarves. How many scarves will each woman have finished? How long will that take?

Answer 1

To solve this problem, we need to find out how many days it will take for Eliana to catch up to Becky and both have completed the same number of scarves. Let's break it down step by step:

1. Becky has already completed 12 scarves.
2. Becky is making an additional 1 scarf per day.
3. Eliana has not completed any scarves yet.
4. Eliana is making 4 scarves per day.
5. We want to find the number of scarves each woman will have finished when Eliana catches up to Becky.

First, let's determine the number of days it will take for Eliana to catch up to Becky:

Let's assume it takes 'x' number of days for Eliana to catch up to Becky.
During these 'x' days, Becky will make 'x' more scarves as she commits to making 1 more scarf per day.
So, the number of scarves Becky will have made in 'x' days will be 12 + x.

Similarly, during these 'x' days, Eliana will make 4 scarves per day. So, the number of scarves Eliana will have made in 'x' days will be 4x.

Now, we need to find the value of 'x' when the number of scarves they both made are equal. We can set up the equation:

12 + x = 4x

Now, let's solve this equation to find the value of 'x':

Subtract 'x' from both sides of the equation:

12 = 3x

Divide both sides of the equation by 3:

12/3 = x
4 = x

So, it will take 4 days for Eliana to catch up to Becky.

To find the number of scarves each woman will have finished, we can substitute the value of 'x' into the equations we set up earlier:

Becky: 12 + x = 12 + 4 = 16 scarves
Eliana: 4x = 4 * 4 = 16 scarves

Therefore, both Becky and Eliana will have finished 16 scarves each when Eliana catches up to Becky, and it will take 4 days for that to happen.