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A girl, A, took 5 hours to paint a wall. Her friend, B, took twice as much time as A to paint a wall of the same dimensions. How long would the task have taken the girls if they had worked together?
Number of hours to finish the task if the friends worked together: x Number of hours for Friend A to finish the task: 5 Number of hours for Friend B to finish the task: 2(5) = 10
Equation for Combined Work (task): 1/5 + 1/10 = 1/x
LCM (Least Common Multiple): 10x
Multiply each term by 10x, then simplify: (10x)(1/5) + (10x)(1/10) = (10x)(1/x) 2x + x = 10 3x = 10 3x/3 = 10/3 x = 10/3 or 3 ¹/₃ hours
ANSWER: It would take 3 ¹/₃ hours for the two friends to finish the task of painting the wall of the same dimensions.
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