Final answer:
Marta can vacuum the house in 40 minutes, and her daughter in 60 minutes. Working together, they would take 24 minutes to vacuum the house by combining their work rates and calculating the joint effort required.
Step-by-step explanation:
The question is asking how long it would take Marta and her daughter to vacuum the house if they worked together. To solve this, we can use the concept of rates in which tasks are completed. We convert their individual working times into work rates per minute, find the sum of these rates to get the combined work rate, and then calculate the total time based on this combined rate.
Marta's rate is 1 house per 40 minutes which is 1/40 house/min, while her daughter's rate is 1 house per 60 minutes which is 1/60 house/min. The combined rate of working together is the sum of their individual rates, which is 1/40 + 1/60 = (3 + 2)/120 = 5/120 = 1/24. This means together, they can vacuum the house at the rate of one house every 24 minutes. Therefore, it would take them 24 minutes to vacuum the house together.