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Sam is painting a room. He can paint $20$ square feet in an hour, while his friend James can paint $30$ square feet in an hour. If they work together, how long will it take them to paint a room that is $300$ square feet?

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Solve proportions: word problems

Full solution

Q. Sam is painting a room. He can paint

20

square feet in an hour, while his friend James can paint

30

square feet in an hour. If they work together, how long will it take them to paint a room that is

300

square feet?

Calculate Combined Painting Rate: Determine the combined painting rate of Sam and James. $\newline$ Sam's rate = $20$ square feet per hour. $\newline$ James's rate = $30$ square feet per hour. $\newline$ Combined rate = Sam's rate + James's rate. $\newline$ Combined rate = $20 + 30 = 50$ square feet per hour.
Determine Time to Paint Room: Calculate the time it will take for them to paint the room together. $\newline$ Total area to be painted = $300$ square feet. $\newline$ Time = Total area / Combined rate. $\newline$ Time = $300 / 50$ . $\newline$ Time = $6$ hours.

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