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All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

 May 25, 2024
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Given that 15 members can paint the wall in 45 minutes, we can calculate the rate at which one member paints the wall.Let's denote the rate at which one member paints the wall as R (wall per minute). If 15 members paint the wall in 45 minutes, then the combined rate of all 15 members is 15R. So, 15R = 1 wall painted in 45 minutes. Thus, the rate of one member painting the wall is R = 1/15 wall per minute.

 

Now, we need to find out how long it would take 20 members to paint the same wall. Let T be the time (in minutes) it would take 20 members to paint the wall. The combined rate of all 20 members is 20R, and we know that the rate of one member is R = 1/15 wall per minute.

 

Therefore, 20R = 20/15 = 4/3 walls per minute. We want to find out how long it would take 20 members to paint 1 wall, so we set up the equation: T * (4/3) = 1. Solving for T: T = 3/4 minutes.
 

Therefore, it would take 20 members 3/4 minutes to paint the wall.

 May 25, 2024

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