https://file.aiquickdraw.com/mathbot/file/1727101712658mh8tbz9n.jpg

Let's break down the problem from the image:

- Twin brothers Billy and Bobby can mow the lawn together in 107 minutes.
- Billy can mow the lawn by himself 20 minutes faster than Bobby.

We need to find how long it would take Bobby to mow the lawn by himself.

### Steps:
1. **Let \( x \)** represent the time it takes Bobby to mow the lawn by himself.
2. Billy takes 20 minutes less than Bobby, so the time Billy takes is \( x - 20 \) minutes.
3. The rate at which Bobby mows the lawn is \( \frac{1}{x} \) lawns per minute.
4. The rate at which Billy mows the lawn is \( \frac{1}{x - 20} \) lawns per minute.
5. Together, they mow the lawn in 107 minutes, so their combined rate is \( \frac{1}{107} \) lawns per minute.

Thus, the equation becomes:

\[
\frac{1}{x} + \frac{1}{x - 20} = \frac{1}{107}
\]

Now, I’ll solve this equation to find \( x \), the time it takes for Bobby to mow the lawn by himself.

Let me compute this.It would take Bobby approximately **10 minutes** to mow the lawn by himself.

Would you like further clarification on any part of the solution? Here are some related questions:

1. How do we derive and simplify equations involving rates of work?
2. How would the result change if Billy mowed 30 minutes faster than Bobby?
3. What would the equation look like if they worked at different times of day with different rates?
4. Can this type of problem be solved graphically instead of algebraically?
5. How would this equation change if the total time mowing together was increased or decreased?

**Tip:** In work problems, always think in terms of rates, i.e., how much work is completed per unit of time, and set up your equation accordingly.

Twin brothers, Billy and Bobby, can mow their grandparents' lawn together in 107 minutes. Billy could mow the lawn by himself in 20 minutes less time than it would take Bobby. How long would it take Bobby to mow the lawn by himself?

Learn how to solve a time and work problem where two brothers, Billy and Bobby, can mow a lawn together in 107 minutes, and Billy mows faster by 20 minutes. Discover how long it would take Bobby to complete the task by himself with detailed algebraic steps. Suitable for students in Grades 7-10.

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