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Question 955974: Person A can paint the neighbor's house 5 times as fast as Person B. The year A and B worked together, it took them 7 days. How long would it take each to paint the house?
Found 3 solutions by lwsshak3, ikleyn, josgarithmetic:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Person A can paint the neighbor's house 5 times as fast as Person B. The year A and B worked together, it took them 7 days. How long would it take each to paint the house?
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let x=number of days A can finish painting the house by himself
his work rate=1/x
5x=number of days B can finish painting the house by himself
his work rate=1/5x
7=number of days both A and B working together can finish painting
Their work rate=1/7
..
sum of indv. work rates=work rate working together
lcd:5x
5+1=5x/7
5x=42
x=42/5=8.4
5x=42
number of days A can finish painting the house by himself=8.4
number of days B can finish painting the house by himself=42
Answer by ikleyn(53889)  (Show Source):
You can put this solution on YOUR website! .
Person A can paint the neighbor's house 5 times as fast as Person B.
The year A and B worked together, it took them 7 days. How long would it take each to paint the house?
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In his post, @lwsshar3 solved the problem, using equations.
Actually, this problem is very simple and is arithmetical in its nature.
In other words, it can be solved MENTALLY, using arithmetic and common sense only, without involving equations.
Such mental solutions develop the childs' minds very much, making them more flexible and stronger.
It is why I can not resist to provide this mental solution here.
Person A works as 5 copies of person B.
So, the team "A+B' works as productive as 6 copies of B.
So, from the problem, 6 copies of B can make the job in 7 days.
Hence, one single B will complete the whole job in 6*7 = 42 days.
From it, one single A will complete the job 5 time faster, in 42/5 = 8  = 8.4 days.
At this point, the problem is solved completely: mentally and without using equations.
Answer by josgarithmetic(39825) (Show Source):
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