# 1. An experienced employee can enter tax data into a computer twice as fast as a new em- ployee. Working together, it takes the employees 2 hr. How long would it take the experi- enced employee working alone? 2. One roofer can put a new roof on a house three times faster than another. Working to- gether, they can roof a house in 4 days. How long would it take the faster roofer working alone? 3. One pipe can fill a swimming pool in 6 hr, and another pipe can do it in 9 hr. How long will it take the two pipes working together to fill the pool full?

1
by benzema

2015-05-25T13:32:57+05:30

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Experienced employee : productivity =  1 / X  amount of work per  hour
he can complete work in X hours
new employee = 1/(2X)    per hour

Working together productivity =  1/X + 1/2X  = 3/2X
=> it takes  2X/3 number of days to complete the work.
=>  2X/3 = 2 hours          =>  X = 3 hours
experience person takes 3 hours and  new one takes 6 hours

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one roofer experience takes X  days..    the other takes 3 X  days
productivity working together =  1/X + 1/3X = 4/(3X)
=> together they take :  3X/4  = 4 days
=> X = 16/3 days      slower one takes :  16 days
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pipe1 :  filling speed = 1/6  per hour
pipe2 :  speed = 1/9  per hour
filling speed when they are together :    1/6 + 1/9 = 5/18  per hour
=>  it takes 18/5 = 3.6 hours  for both together