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# rate problem

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If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

Feb 10, 2020

#1
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6 minutes 40 sec  =  400 sec

So.....each second the  cold  water fills 1/400 of the tub

8 minutes  =  480 sec

So....each second the  hot water fills  1/480  of the  tub

And  13 min 20 sec  =  800 sec

So....each second, 1/800  of the  tub  is drained

So....we  need to  solve this.....where x is the  number of seconds it takes to  fill the tub

(1/400)x + ( 1/480)x  - (1/800)x   =  1

(2/800)x  + (1/480)x - (1/800)x   = 1

(1/800)x  + (1/480) x  = 1

[ 480 + 800] x / { 800 * 480)   = 1

x  =  (800 * 480)  / { 480 + 800)    =  300 sec  to  fill the  tub =  5 minutes   Feb 10, 2020