SOLUTION: A wind generator can charge 20 storage batteries in 24 h . After the generator has been charging for 6.0 h , another generator, which can charge the batteries in 36 h , is also c

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A wind generator can charge 20 storage batteries in 24 h . After the generator has been charging for 6.0 h , another generator, which can charge the batteries in 36 h , is also c      Log On


   

Question 1055498: A wind generator can charge 20 storage batteries in 24 h . After the generator has been charging for 6.0 h , another generator, which can charge the batteries in 36 h , is also connected to the batteries. How many additional hours are needed to charge the 20 batteries?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of charging for the wind
generator is [ 1 pack ] / [ 24 hrs ]
( I can call the 20 storage batteries 1 pack
because the problem is only about the 20
batteries, never more & never less. )
---------------------------------------
The fraction of charging after 6 hrs is:
+6%2A%28+1%2F24+%29+=+1%2F4+
There is +1+-+1%2F4+=+3%2F4+ of the charging job
left to do
-------------------------------------------
Now you have 2 generators charging the pack.
Add their rates of charging.
Let +t+ = time to do the +3%2F4+ of the charging job
+1%2F24+%2B+1%2F36+=+%28%283%2F4%29%29%2Ft+
Multiply both sides by +72t+
+3t+%2B+2t+=+3%2A18+
+5t+=+54+
+t+=+10.8+
-------------------------------
10.8 additional hours are needed
to charge the 20 batteries
-------------------------------
check:
+1%2F24+%2B+1%2F36+=+%28%283%2F4%29%29%2Ft+
+1%2F24+%2B+1%2F36+=+%28%283%2F4%29%29%2F10.8+
+.0416667+%2B+.027777+=+.069444+
+.0694437+=+.069444+
error due to rounding off, I think
OK