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The problem states that:

- Brad and Angelina together can mow the lawn in **20 minutes**.
- Brad alone can mow the lawn in **45 minutes**.
- We need to determine how long it would take Angelina to mow the lawn by herself.

Let’s define the rates of work:

- Brad’s rate of work is \( \frac{1}{45} \) lawns per minute (since it takes him 45 minutes to mow 1 lawn).
- Let Angelina’s rate of work be \( \frac{1}{A} \) lawns per minute, where \( A \) is the number of minutes it takes Angelina to mow the lawn alone.

When they work together, their combined rate is \( \frac{1}{45} + \frac{1}{A} \), and this combined rate equals \( \frac{1}{20} \) lawns per minute since together they can mow the lawn in 20 minutes.

Thus, the equation is:

\[
\frac{1}{45} + \frac{1}{A} = \frac{1}{20}
\]

Now, let's solve for \( A \).The solution to the equation is \( A = 36 \), meaning it would take Angelina **36 minutes** to mow the lawn by herself.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this concept:

1. What if Brad could mow the lawn alone in 30 minutes instead of 45? How long would it take Angelina?
2. What if Brad and Angelina together could mow the lawn in 15 minutes? How would that change Angelina’s time?
3. If Angelina could mow the lawn in 36 minutes but had a second identical mower, how long would it take her to mow the lawn?
4. What if they worked at variable rates over time? How could we model that scenario mathematically?
5. What other real-life tasks can be modeled using rates of work like this?

**Tip:** When solving word problems with rates, it's often helpful to think in terms of "work done per unit of time" to set up the equations correctly.

Brad and Angelina can mow their yard together with two lawn mowers in 20 minutes. When Brad works alone, it takes him 45 minutes. How long would it take Angelina to mow the lawn by herself?

Solve the work rate problem where Brad and Angelina mow their lawn together in 20 minutes, but Brad alone takes 45 minutes. Learn how to calculate Angelina's time to mow the lawn by herself using the combined work formula.

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