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To solve the problem, we need to determine how long it will take Vince and Janno to paint the house together.

### Step 1: Work rates of Vince and Janno
- Vince can paint the house in 5 days, so his work rate is \( \frac{1}{5} \) of the house per day.
- Janno can paint the house in 4 days, so his work rate is \( \frac{1}{4} \) of the house per day.

### Step 2: Combined work rate
When they work together, their combined work rate is the sum of their individual rates:
\[
\text{Combined work rate} = \frac{1}{5} + \frac{1}{4}
\]
To add these, we find a common denominator:
\[
\frac{1}{5} + \frac{1}{4} = \frac{4}{20} + \frac{5}{20} = \frac{9}{20}
\]
So, together they can complete \( \frac{9}{20} \) of the house per day.

### Step 3: Time to complete the job together
To find how long it will take them to complete the entire job, we take the reciprocal of the combined rate:
\[
\text{Time to finish} = \frac{1}{\frac{9}{20}} = \frac{20}{9} \text{ days}
\]
This simplifies to approximately 2.22 days.

### Conclusion:
Vince and Janno, working together, can finish the job in **\( \frac{20}{9} \) days**, or approximately **2.22 days**.

Would you like a deeper explanation of any step? Here are some related questions you might want to explore:

1. What is the work rate formula for similar problems?
2. How do you find a common denominator when adding fractions?
3. How does the reciprocal of a rate give time?
4. Can this method be applied to more than two workers?
5. What if one of them takes breaks, how would that affect the calculation?

**Tip:** When solving work rate problems, adding individual rates is a quick way to determine the total rate when people work together.

Vince can paint a house in 5 days and Janno can do the same work in 4 days. How long will it take them to finish the same work if they work together?

Learn how to solve a work rate problem where Vince can paint a house in 5 days, and Janno can do it in 4 days. Find out how long it will take them to complete the job together using their combined work rates. Suitable for students in Grades 7-9.

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