SOLUTION: A tub can be filled with hot water in 9 minutes, or with cold water in 6 minutes. The tub can also be emptied when the plug is pulled out, in 4 minutes. Farley ran the hot water in

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tub can be filled with hot water in 9 minutes, or with cold water in 6 minutes. The tub can also be emptied when the plug is pulled out, in 4 minutes. Farley ran the hot water in      Log On


   

Question 1099371: A tub can be filled with hot water in 9 minutes, or with cold water in 6 minutes. The tub can also be emptied when the plug is pulled out, in 4 minutes. Farley ran the hot water in his tub for 3 minutes, then both the cold and hot water together for 1 minute, and then with the two taps still running, he accidentally pulled the plug. How long, did it take in minutes, for the tub to fill after the plug was pulled?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
PIPE          RATE in TUB per MINUTES

hot tap        1%2F9
cold tap       1%2F6
drain         -1%2F4




x, unknown time to finish filling tub while all three pipes were open
%281%2F9%29%2A3%2B%281%2F9%2B1%2F6%29%2A1%2B%281%2F9%2B1%2F6-1%2F4%29%2Ax=1
-
1%2F3%2B1%2F9%2B1%2F6%2B%281%2F9%2B1%2F6-1%2F4%29x=1
LCD=36;
12%2B4%2B6%2B%284%2B6-9%29x=36
22%2Bx=36
x=36-22
highlight%28x=14%29
fourteen minutes

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
He ran the hot water for +3+ min
The tub was then +3%2F9+=+1%2F3+ filled
+2%2F3+ of the tube still empty
-------------------------------------
He ran both hot and cold water for +1+ min
+1%2F9+%2B+1%2F6+=+x%2F1+ where +x+ =
The fraction of +2%2F3+ of the tub filled
in +1+ min
----------------------
Multiply both sides by +6%2A9+=+54+
+6+%2B+9+=+54x+
+x+=+15%2F54+
+x+=+5%2F18+
and
+%28+5%2F18+%29%2A%28+2%2F3+%29+=+5%2F27+
There is
+9%2F27+%2B+5%2F27+=+14%2F27+ filles
There is +13%2F27+ left to be filled
-------------------------------------
+1%2F9+%2B+1%2F6+-+1%2F4+=+%28+13%2F27+%29%2Ft+
Multiply both sides by +108t+
+12t+%2B+18t+-+27t+=+52+
+3t+=+52+
+t+=+17.333+ min
+.333%2A60+=+20+ sec
It takes 17 min and 20 sec to fill the tub
after the plug was pulled
------------------------------------------
Definitely get a 2nd opinion on this.
I could easily make a mistake!