It will take you 10 hours to paint your garage and it will take your brother 15 hours to do the same job. How long will it take if the two of you together to paint the garage?

To solve this problem, we can use the concept of work rates. 

Your rate of painting is \( \frac{1}{10} \) of the garage per hour, and your brother's rate is \( \frac{1}{15} \) of the garage per hour. When working together, the rates add up.

1. Your rate: \( \frac{1}{10} \) (fraction of the garage per hour)
2. Your brother's rate: \( \frac{1}{15} \) (fraction of the garage per hour)

Together, your combined rate is:

\[
\frac{1}{10} + \frac{1}{15}
\]

To add these fractions, first find a common denominator:

\[
\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}
\]

So, together, you both can paint \( \frac{1}{6} \) of the garage per hour.

The time it will take to paint the entire garage together is the reciprocal of your combined rate:

\[
\text{Time} = \frac{1}{\frac{1}{6}} = 6 \text{ hours}
\]

### Answer: It will take 6 hours for both of you to paint the garage together.

Do you want more details or have any questions?

---

Here are 5 related questions to consider:
1. What if you work faster, completing the garage in 8 hours instead of 10?
2. How long would it take if your brother had some help and finished in 12 hours instead of 15?
3. What if you work for 4 hours together, then finish the rest alone—how long would it take?
4. How much of the garage would be painted after 3 hours of working together?
5. What would happen if your brother took breaks and only worked half the time?

**Tip**: When combining work rates, always add the rates first, and then find the reciprocal to get the total time required for the job.

It will take you 10 hours to paint your garage and it will take your brother 15 hours to do the same job. How long will it take if the two of you together to paint the garage?

Learn how to solve a common work rate problem where two people, one taking 10 hours and the other 15 hours, work together to paint a garage. Understand the key concepts of adding work rates and using reciprocals to find the total time. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation