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# Maths

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A cold water tap takes 3 minutes to fill the bath. A hot water tap takes 2 minutes to fill the bath. How long does it take to fill the bath when both taps are open at the same time?

Sep 22, 2018

#1
+102459
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A cold water tap takes 3 minutes to fill the bath. A hot water tap takes 2 minutes to fill the bath. How long does it take to fill the bath when both taps are open at the same time?

It is easiest just to let the bath be a given size.

My little bath will be 12 litres

cold water  4L/min          hot water = 6L/min

together 10L/1 min

10*(12/10) L per  1*(12/10) minutes

12L per 1.2min

12L per 1min and 12sec

It will take 1 minute and 12 seconds to fill the bath.

Sep 22, 2018
#2
+3

Here is another simple way:

1/3 + 1/2 =5/6. Then flip 5/6 to 6/5 =1.2 minutes to fill the bathtub.

If it takes the cold water 3 minutes to fill the bathtub, then in 1 minute it will fill 1/3 of the bathtub.
Similarly, the same applies to hot water, or in 1 minute it will fill 1/2 of the bathtub.
So, the 2 taps combined in 1 minute will fill: 1/3 of the bathtub + 1/2 of the bathtub=5/6 of the tub in 1 minute.
So, the time it takes to fill the entire bathtub will be: 1 / (5/6) =1 x 6/5 =6/5 =1.2 minutes to fill the entire bathtub.

Sep 22, 2018
edited by Guest  Sep 22, 2018
#3
+102459
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Guest i think you should explain your method.

If you cannot explain it then that means you do not understand why it works.

Melody  Sep 22, 2018
#4
+18457
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Cold RATE for 1 bath = 1/3 b/m   b = bath   m=minutes

Hot  RATE for 1 bath = 1/2 b/m

Rate x time = volume

We want volume = 1  bath       (1/3 b/m + 1/2 b/m) *x = 1 b         b= bath     x = time to fill (in minutes)

(1/3+1/2)x =1

(2/6 + 3/6) x = 1

5/6 x = 1

x = 6/5 min       =   1 min 12 sec

Sep 22, 2018
#5
+101871
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Note that  1/3 of the bath is filled by the frist tap each minute  and  1/2  of the bath is filled by the second tap each minute

So...the   fraction filled by both taps in one minute is (1/3) + (1/2)  =  5/6

Invert this fraction  to find the number of minutes to fill the bath  =  6/5 minutes  = 1 + 1/5  minutes =  1 min, 12 seconds  [as Melody,  Guest and  EP found !! ]

Note that the method works because   if , for example, 1/2 of the bath were filled in one minute,  the reciprocal of this fraction  tells us how many minutes it would take to  fill the bath  = 2/1   = 2  minutes  !!!

Sep 22, 2018
edited by CPhill  Sep 22, 2018