SOLUTION: A pump was used to empty a flooded basement. After 3 hours, a second bump was added and the basement was emptied in 8 more hours. The first pump could have done the job alone in 20

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pump was used to empty a flooded basement. After 3 hours, a second bump was added and the basement was emptied in 8 more hours. The first pump could have done the job alone in 20      Log On


   

Question 846348: A pump was used to empty a flooded basement. After 3 hours, a second bump was added and the basement was emptied in 8 more hours. The first pump could have done the job alone in 20 hours.How long would it take the second pump to do the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you add the 2 pump's rate of pumping,
you get their rate pumping together
--------------------------------
The rate of the 1st pump was:
( 1 basement pumped ) / ( 20 hrs )
------------------------------
Let +t+ = the time in hours for the
2nd pump to pump out the basement
after 3 hrs
--------------------------------
In 3 hours, the 1st pump pumps out
+3%2A%28+1%2F20+%29+=+3%2F20+ of the basement
That means there is +17%2F20+ of
the basement left to pump out
---------------------------------
+1%2F20+%2B+1%2Ft+=+%28%28+17%2F20%29%29+%2F+8+
+1%2F20+%2B+1%2Ft+=+17%2F160+
Multiply both sides by +160t+
+8t+%2B+160+=+17t+
+9t+=+160+
+t+=+17.7778+
+.7778%2A60+=+47+
The 2nd pump alone can pump out the
basement in 17 hrs and 47 minutes
check:
+1%2F20+%2B+1%2Ft+=+17%2F160+
+1%2F20+%2B+1%2F17.7778+=+17%2F160+
+.05+%2B+.05625+=+.10625+
+.10625+=+.10625+
OK