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?
a. 16
b. 12
c. 8.6
d. 5
e. 4.75
OA = D
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Water Draining rates problem
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tonebeeze
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Time for cold water = 400 seconds.tonebeeze wrote: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?
a. 16
b. 12
c. 8.6
d. 5
e. 4.75
OA = D
Time for hot water = 480 seconds.
Time for drain = 800 seconds.
Let tub = 2400 liters.
Rate for cold water = w/t = 2400/400 = 6 liters per second.
Rate for hot water = w/t = 2400/480 = 5 liters per second.
Rate for drain = w/t = 2400/800 = 3 liters per second.
Combined rate for cold+hot = 6+5 = 11 liters per second.
Since the drain is competing with the cold and hot water, its rate must be subtracted: 11-3 = 8 liters per second.
With all three running together, time to fill the tub = w/r = 2400/8 = 300 seconds = 5 minutes.
The correct answer is D.
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pemdas
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speed problem -> 1/400 sec cold water speed and 1/480 hot water speed, double speed 11/(80*30)
drainage speed -> 1/800
1: (11/(80*30) - 1/800)= (80*30)/(11-3)=300 sec or 5 min.
IOM d
drainage speed -> 1/800
1: (11/(80*30) - 1/800)= (80*30)/(11-3)=300 sec or 5 min.
IOM d
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kevincanspain
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time needed for C to fill tub= 20/3 min , thus C fills 3/20 of tub in 1 mintonebeeze wrote: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?
a. 16
b. 12
c. 8.6
d. 5
e. 4.75
OA = D
Similarly H fills 1/8 of tub in 1 min
D empties 3/40 in 1 min
3/20 + 1/8 - 3/40 = 8/40= 1/5
Thus 1/5 of tub in filled in 1 minute if both taps are running and drain in open
Choose D
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