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?

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Cessantasudaid Cessantasudaid

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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?

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Анонимid Анонимid · Answer 1

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.