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The problem on your screen involves a typical work-rate question. Here's how you can approach it:

### Problem Breakdown:
- A person can mow the lawn by himself in 80 minutes. So, his rate of work is \( \frac{1}{80} \) lawns per minute.
- When his daughter helps, they can mow the lawn together in 60 minutes. So, their combined rate of work is \( \frac{1}{60} \) lawns per minute.
- We need to determine how long it would take his daughter to mow the lawn by herself. Let’s denote her time to mow the lawn alone by \( x \) minutes. Therefore, her rate of work is \( \frac{1}{x} \) lawns per minute.

### Equation Setup:
The combined work rate of both the person and his daughter working together is the sum of their individual work rates:
\[
\frac{1}{80} + \frac{1}{x} = \frac{1}{60}
\]
We can solve this equation to find \( x \).

### Step 1: Subtract the person’s rate from both sides:
\[
\frac{1}{x} = \frac{1}{60} - \frac{1}{80}
\]

### Step 2: Find a common denominator and simplify the right-hand side:
The least common denominator of 60 and 80 is 240. Rewriting the fractions:
\[
\frac{1}{60} = \frac{4}{240}, \quad \frac{1}{80} = \frac{3}{240}
\]
So, the equation becomes:
\[
\frac{1}{x} = \frac{4}{240} - \frac{3}{240} = \frac{1}{240}
\]

### Step 3: Solve for \( x \):
\[
x = 240
\]

### Conclusion:
It would take his daughter **240 minutes** to mow the lawn by herself.

Would you like a detailed explanation of any specific step? Here are some related questions for further practice:

1. If the person and his daughter mow the lawn together in 50 minutes, how long would it take her to mow it alone?
2. What would happen if the person mows the lawn in 100 minutes and they finish together in 70 minutes?
3. What if three people were mowing the lawn together, how would you set up the equation?
4. How would this problem change if we wanted to find how much of the lawn they could mow in 40 minutes working together?
5. Can you express this kind of problem in terms of percentages of the lawn mowed?

**Tip:** Always simplify equations involving rates by finding the least common denominator—this helps avoid unnecessary complexity in solving the problem.

By himself, a person can mow his lawn in 80 minutes. If his daughter helps, they can mow the lawn together in 60 minutes. How long would it take his daughter to mow the lawn by herself?

Learn how to solve a work-rate problem where a person and his daughter mow a lawn together. This problem covers algebraic concepts including work rate equations and is suitable for students in Grades 8-10.

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