Question

You can paint a certain room in 7 hours. Your brother can do it in 2 hours. How long does it take the two of you working together?

Hint: Call u the number of hours it will take the two of you. Think about how much of the room you and your brother
each can paint in one hour.

Answer 1

Answer as an improper fraction = 14/9 hours

Answer as a mixed number = 1 & 5/9 hours

Answer as an approximate decimal = 1.556 hours

Likely you'll only pick one answer format. It will depend on what your teacher prefers.

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Explanation:

Let's say we're dealing with 140 square feet of walls and ceiling to paint. I picked this number because 7*2 = 14, and then I added a 0 at the end. I'm doing this to ensure we get whole number results in the next sections below.

If you have 140 square feet of walls/ceiling to paint, and you can do it in 7 hours, then your unit rate is 140/7 = 20 sq ft per hour.

Your brother can do the same job in 2 hours, meaning his rate is 140/2 = 70 sq ft per hour.

The combined rate is 20+70 = 90 sq ft per hour. This is assuming neither of you hinder one another (i.e. you both don't slow each other down or get in each other's way).

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Let x be the time, in hours, it takes for you both to get the job done if you work together. If your combined unit rate is 90 sq ft per hour, then you can paint 90x square feet of walls/ceiling in x hours.

Set this equal to the 140 value we set up earlier and solve for x.

90x = 140

x = 140/90

x = 14/9

x = 1.556 approximately

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Side note: The improper fraction 14/9 converts to the mixed number 1 & 5/9 because of these steps here

14/9 = (9+5)/9

14/9 = 9/9 + 5/9

14/9 = 1 + 5/9

14/9 = 1 & 5/9

Answer 2

Answer:

x = time for both to do job then

x(1/3 + 1/4) = 1

multiplying both sides by 12:

x(4 + 3) = 12

7x = 12

x = 12/7 hours or

x = 1 hour 43 minutes

Hope this helped! :)