3 men finish painting a wall in 8 days. Four boys do the same job in 7 days. In how many days will 2 men and 2 boys working together paint two such walls of the same size?
Question
3 men finish painting a wall in 8 days. Four boys do the same job in 7 days. In how many days will 2 men and 2 boys working together paint two such walls of the same size?
Solution
Sure, let's solve this step by step:
Step 1: Find the rate at which 3 men can paint a wall. Since 3 men can paint a wall in 8 days, 1 man can paint the same wall in 3*8 = 24 days.
Step 2: Find the rate at which 4 boys can paint a wall. Since 4 boys can paint a wall in 7 days, 1 boy can paint the same wall in 4*7 = 28 days.
Step 3: Find the combined rate of 2 men and 2 boys. Since 1 man can paint a wall in 24 days, 2 men can do it in 24/2 = 12 days. Similarly, since 1 boy can paint a wall in 28 days, 2 boys can do it in 28/2 = 14 days. So, 2 men and 2 boys can paint a wall in 1/(1/12 + 1/14) = 6.545 days (approximately).
Step 4: Since 2 men and 2 boys can paint a wall in 6.545 days, they can paint two such walls in 2*6.545 = 13.09 days (approximately). So, it will take them around 13 days to paint two walls of the same size.
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