SOLUTION: Three machines are filling water bottles. The machines can fill the daily quota of water bottles in 90 h, 99 h, and 110 h, respectively. How long would it take to fill the daily qu

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Question 1028975: Three machines are filling water bottles. The machines can fill the daily quota of water bottles in 90 h, 99 h, and 110 h, respectively. How long would it take to fill the daily quota of water bottles with all three machines working?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling
to get rate filling together
rate fore each machine =
[ daily quota ] / [ time to fill the quota ]
Let +t+ = time in hrs to fill quota
with all 3 machines working
+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2Ft+
Multiply both sides by +90%2A99+%2A110%2At+
+99%2A110%2At+%2B+90%2A110%2At+%2B+90%2A99%2At+=+90%2A99%2A110+
+10890t+%2B+9900t+%2B+8910t+=+980100+
+29700t+=+980100+
+t+=+33+
with all three machines working, you can
fill the daily quota of water bottles in 33 hrs
-------------------
check answer:
+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2Ft+
+1%2F90+%2B+1%2F99+%2B+1%2F110+=+1%2F33+
+.011111+%2B+.010101+%2B+.009090+=+.030303+
+.030302+=+.030303+
OK -error due to rounding off

Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.
Three machines are filling water bottles. The machines can fill the daily quota of water bottles in 90 h, 99 h, and 110 h, respectively.
How long would it take to fill the daily quota of water bottles with all three machines working?
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The first machine can fill 1%2F90 of the daily quota of bottles in one hour (in each hour). It is its rate of work.

The second machine can fill 1%2F99 of the daily quota of bottles in one hour (in each hour). It is its rate of work.

The third machine can fill 1%2F110 of the daily quota of bottles in one hour (in each hour). It is its rate of work.

If all three machines works simultaneously, they fill 

1%2F90+%2B+1%2F99+%2B+1%2F110 = 11%2F990+%2B+10%2F990+%2B+9%2F990 = %2811%2B10%2B9%29%2F990 = 30%2F990 = 1%2F33

of the daily quota of bottles in one hour (in each hour). 

Hence, it will take 33 hours for the three machine to fill the daily quota of bottles working simultaneously.