Let’s break this problem down step-by-step.

Step 1: Calculate the rate of work for Brandy and Lisa

• Brandy takes 6 hours to repair a computer. This means her rate of work is: $\text{Brandy's rate} = \frac{1 \text{ computer}}{6 \text{ hours}} = \frac{1}{6} \text{ of a computer per hour.}$
• Lisa takes 4 hours to repair a computer. Her rate of work is: $\text{Lisa's rate} = \frac{1 \text{ computer}}{4 \text{ hours}} = \frac{1}{4} \text{ of a computer per hour.}$

Step 2: Find the combined rate of work for Brandy and Lisa

When they work together for 1 hour, we can add their rates: $\text{Combined rate} = \frac{1}{6} + \frac{1}{4}$ To add these fractions, we find a common denominator. The least common denominator (LCD) of 6 and 4 is 12: $\frac{1}{6} = \frac{2}{12}, \quad \frac{1}{4} = \frac{3}{12}$ So, $\text{Combined rate} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}$ Thus, together they can repair $\frac{5}{12}$ of a computer per hour.

Step 3: Calculate the work done in 1 hour

In 1 hour of working together, they complete $\frac{5}{12}$ of the computer.

Step 4: Calculate how much work is left for Brandy

Since they complete $\frac{5}{12}$ of the work together, the remaining work to finish the computer is: $1 - \frac{5}{12} = \frac{12}{12} - \frac{5}{12} = \frac{7}{12}$ So, Brandy needs to finish $\frac{7}{12}$ of the computer on her own.

Step 5: Find how long it takes Brandy to finish the remaining work

Brandy’s rate is $\frac{1}{6}$ of a computer per hour. To find how long it takes her to finish $\frac{7}{12}$ of the computer, we use the formula: $\text{Time} = \frac{\text{Work remaining}}{\text{Rate}} = \frac{\frac{7}{12}}{\frac{1}{6}} = \frac{7}{12} \times \frac{6}{1} = \frac{42}{12} = 3.5 \text{ hours.}$

Step 6: Calculate the total time Brandy worked

Brandy worked 1 hour with Lisa and then 3.5 hours to finish the computer on her own. So, the total time Brandy worked is: $1 + 3.5 = 4.5 \text{ hours.}$

Final Answer:

Brandy spent a total of 4.5 hours working to repair the computer.

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Would you like further clarification or details? Here are some related questions:

1. How long would it take Lisa to repair the computer if she worked alone after Brandy helped for 1 hour?
2. If Brandy and Lisa worked together for 2 hours, how much of the repair would be done?
3. How much work would Lisa complete if she worked alone for 3 hours?
4. How much faster would it be for Brandy and Lisa to finish the repair if they both worked together for 3 hours?
5. What if the repair job was only 3/4 of the computer—how long would it take Brandy and Lisa together?

Tip: When combining rates of work, always find a common denominator to add fractions, and remember that time is the remaining work divided by the rate of work.