Questions: Sally can paint a room in 8 hours while it takes Steve 9 hours to paint the same room. How long would it take them to paint the room if they worked together? It would take hours. (Type an integer or decimal rounded to one decimal place as needed.)

Sally can paint a room in 8 hours while it takes Steve 9 hours to paint the same room. How long would it take them to paint the room if they worked together? It would take hours. (Type an integer or decimal rounded to one decimal place as needed.)
Transcript text: Question Sally can paint a room in 8 hours while it takes Steve 9 hours to paint the same room. How long would it take them to paint the room if they worked together? It would take $\square$ hours. (Type an integer or decimal rounded to one decimal place as needed.)
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Solution

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Solution Steps

Step 1: Calculate the rate of work for each person

For Person A, the rate of work is \(1/T_A = 1/8 = 0.125\) task per hour. For Person B, the rate of work is \(1/T_B = 1/9 = 0.111\) task per hour.

Step 2: Calculate the combined rate of work

The combined rate of work when both are working together is \(Rate_{combined} = 1/T_A + 1/T_B = 0.125 + 0.111 = 0.236\) tasks per hour.

Step 3: Calculate the time it takes for both to complete the task together

The time for both to complete the task together is \(T_{together} = 1 / Rate_{combined} = 1 / 0.236 = 4.2\) hours.

Final Answer:

It takes 4.2 hours for both individuals to complete the task together when rounded to 1 decimal places.

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