A full bathtub will empty at an average rate of 10 minutes. It will fill up to full at an average rate of 8 minutes if the plug is in. How long will it take to fill up to full if the plug is removed and the tap is turned on?
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2
Filling the tub in 8 minutes:
1/8 of the job in 1 minute.
Emptying 10 minutes
1/10 of this job in 1 minute.
1/8 -1/10 = effective filling in 1 minute
LCM= 40
(5-4)/40=1/40 of the job of filling in 1 minute.
So when plug is open it will take 40/1 minutes
40 minutes to fill the tub.
1/8 of the job in 1 minute.
Emptying 10 minutes
1/10 of this job in 1 minute.
1/8 -1/10 = effective filling in 1 minute
LCM= 40
(5-4)/40=1/40 of the job of filling in 1 minute.
So when plug is open it will take 40/1 minutes
40 minutes to fill the tub.
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Answer:
Rate of emptying :
( 1 tub) / ( 10 Min)
Rate of filling with plug in:
( 1 tub ) / ( 8 min )
What you have to realize at this point is
that the rate of filling is greater than the
rate of emptying, so if you pull the plug
out, the tub will EVENTUALLY fill up.
Let +t+ = the time in minutes for the tub
to fill if the tap is on and the plug is removed
Add the rate of filling
Subtract the rate of emptying
Make that equal to :
( 1 tub filled) / (t min)= 1/t
Eventuallly after calculating, you will get 40 minutes for tub to fill if the tap is on and plug is removed.
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