Problema Solution
You are the head of the General Services division of a famous resort in your locality with the widest swimming pool. Five pipes were installed in the pool, three of which are used for filling and the other two for draining. The filling pipes A, B, and C can fill the pool in 9 hours, 7 hours, and 10 hours, respectively. The pool can be drained in 12 hours using pipe D and 15 hours using pipe E.
The one in charge of the swimming pool, Mang Jose, is on vacation when the owner of the resort came and saw some impurities in the pool. The owner immediately directed you to call Mang Jose to change the water. Since Mang Jose is not around, you did the job of changing the water of the pool. When the pool was completely filled, you and the owner observed that the total time it took was longer than the usual time. Because of this, the owner instructed you too make an incident report stating why the total filling time is longer.
Upon inspection, you found out that pipes D and E were open while pipes A,B and C were filling the pool. Your report should contain the computation for the total number of hours it took to fill the swimming pool and its difference from the normal number of hours required to fill the pool.
Answer provided by our tutors
The rate of pipe A is: 1/9 pool per hour
The rate of pipe B is: 1/7 pool per hour
The rate of pipe C is: 1/10 pool per hour
The rate of pipe D is: 1/12 pool per hour
The rate of pipe E is: 1/15 pool per hour
Let 't' represent the normal number of hours needed to fill the pool (when only the filling pipes are open):
t*(1/9) + t*(1/7) + t*(1/10) = 1
........
click here to see the equation solved for t
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t = 2.83 hr
Let 'x' represent the total number of hours need to fill the pool when all the pipes are open:
x(1/9) + x(1/7) + x(1/10) - x(1/12) + x(1/15) = 1
........
click here to see the equation solved for x
........
x = 2.94 hr
The difference is 2.94 - 1.83 = 1.11 hr.
The total number of hours it took to fill the swimming pool is 2.94 hours and the difference from the normal number of hours required to fill the pool is 1.11 hours.