Question

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?

Answer 1

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

====================================

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
====================
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