Question

Elizabeth makes cookies in 10 minutes. Her sister makes cookies in 40 minutes. How long will it take them to make the cookies together?

Answer 1

Elizabeth and her sister have a combined work rate of 0.125 batches per minute when making cookies together. By taking the reciprocal of this rate, we can determine that they will take 8 minutes to make a batch of cookies together.

Step-by-step explanation:

Elizabeth makes cookies in 10 minutes, and her sister makes cookies in 40 minutes. To determine how long it will take them to make cookies together, we need to find their combined work rate. We can use the concept of work rates, where the rate is typically defined as work done per unit of time. In this case, work is the completion of one batch of cookies. Elizabeth's rate is 1 batch/10 minutes, or 0.1 batches per minute. Her sister's rate is 1 batch/40 minutes, or 0.025 batches per minute. Adding these two rates gives us the combined rate, which is 0.1 + 0.025 = 0.125 batches per minute.

To find the time it takes for them to make one batch of cookies together, we take the reciprocal of the combined rate. So, the time is 1 / 0.125, which equals 8 minutes. Therefore, it will take Elizabeth and her sister a total of 8 minutes to make a batch of cookies together.

Answer 2

8 minutes.

Step-by-step explanation:

Let's denote the time it takes Elizabeth to make the cookies by "t1" and the time it takes her sister to make the cookies by "t2". Then we can write:

Elizabeth's rate of work: 1 cookie / 10 minutes = 0.1 cookie/minute

Sister's rate of work: 1 cookie / 40 minutes = 0.025 cookie/minute

When they work together, their rates of work add up:

Combined rate of work: 0.1 cookie/minute + 0.025 cookie/minute = 0.125 cookie/minute

This means that together they can make 0.125 cookies per minute. Let's denote the time it takes them to make the cookies together by "t". Then we can write:

Combined rate of work * time = amount of work done

0.125 cookie/minute * t = 1 cookie (since they want to make one batch of cookies)

Solving for "t", we get:

t = 1 cookie / 0.125 cookie/minute = 8 minutes

Therefore, it will take Elizabeth and her sister 8 minutes to make the cookies together.