A small pipe takes 24 minutes longer to fill a tank than it takes a large pipe. The two pipes together can fill the tank in 9 minutes. How long does it take each pipe alone to fill the tank?

1 Answer
Gió
Oct 13, 2015

I found #36min# for the small and #12min# for the large

Explanation:

Call #s# the carryng capacity in liters/minute of the small pipe and #l# of the large. You can write:
#s=x/t#
#l=x/(t-24)#
#s+l=x/9# where #x# is the capacity of the tank in liters.
Substituting the first 2 into the last:
#x/t+x/(t-24)=x/9# cancel the #x#s:
#1/t+1/(t-24)=1/9#
#(t-24+t)9=t(t-24)#
#18t-216=t^2-24t#
#t^2-42t+216=0#
Using the Quadratic Formula:
#t_1=6min# NO too small
#t_2=36min# YES

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