Question 426337
It takes one day to fill the vat with this large pipe; two days with that'
 The third pipe needs but one day more; The fourth pipe fills the vat in four.
 If all four pipes together run, How many HOURS before the task is done?
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Let's use hrs for this, since it wants the solution in hours
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Let t = time required by all 4 pipes working together
Let the completed job = 1; (a full vat)
:
{{{t/24}}} + {{{t/48}}} + {{{t/72}}} + {{{t/96}}} = 1
The common denominator is 288, multiply thru by that, results:
12t + 6t + 4t + 3t = 288
25t = 288
t = {{{288/25}}}
t = 11.52 hrs for all four to complete the task
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:
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Let's check that to be sure
{{{11.52/24}}} + {{{11.52/48}}} + {{{11.52/72}}} + {{{11.52/96}}} =
.48 + .24 + .16 + .12 = 1; confirms our solution of 11.52 hrs