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?

ZaraBatook
Sep 22, 2018

#1**+3 **

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.

Melody
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.**

Guest Sep 22, 2018

edited by
Guest
Sep 22, 2018

#4**+3 **

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

ElectricPavlov
Sep 22, 2018

#5**+2 **

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 !!!

CPhill
Sep 22, 2018