Miro can paint a plank alone in 6 hours. Miranda can paint the same plank alone in 3 hours How long will it take if they help each other?

To find out how long it will take for Miro and Miranda to paint the plank together, we can use the concept of work rates. Here's how we solve it:

### Step 1: Determine individual work rates
- Miro's work rate: Miro can paint the entire plank in 6 hours. So, Miro's work rate is \(\frac{1}{6}\) of the plank per hour.
- Miranda's work rate: Miranda can paint the entire plank in 3 hours. So, Miranda's work rate is \(\frac{1}{3}\) of the plank per hour.

### Step 2: Add the work rates
When working together, their combined work rate is the sum of their individual work rates:

\[
\text{Combined work rate} = \frac{1}{6} + \frac{1}{3}
\]

To add these fractions, find a common denominator:

\[
\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}
\]

This means that together, Miro and Miranda can paint \(\frac{1}{2}\) of the plank in 1 hour.

### Step 3: Calculate the time
If they can complete \(\frac{1}{2}\) of the plank in 1 hour, it will take them 2 hours to paint the entire plank.

So, **it will take them 2 hours to paint the plank if they work together**.

Would you like further details or have any questions?

Here are 5 related questions to expand this topic:
1. How would the time change if a third person helped, who could paint the plank in 4 hours?
2. What if Miro and Miranda take breaks after every hour? How would that affect the total time?
3. If Miro works twice as fast, how long will it take them together?
4. Can you calculate the fraction of the plank completed in 30 minutes when they work together?
5. How does the concept of work rates apply to different types of tasks, like filling a tank or assembling products?

**Tip:** Always convert tasks into work rates (task per time) when dealing with combined work problems.

Miro can paint a plank alone in 6 hours. Miranda can paint the same plank alone in 3 hours. How long will it take if they help each other?

Learn how to calculate how long it will take for Miro and Miranda to paint a plank together, using work rates. Miro can paint the plank alone in 6 hours, while Miranda can do it in 3 hours. This problem demonstrates how to add work rates and solve for the time taken. Suitable for Grades 5-7.

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