If it takes a old and hot tap 6 mins to fill a bath and on their own it takes the hot tap 100 secs more than the cold tap to fill bath. How long will it take the cold tap on its own to ill the bath

rate of cold tap = 1/x , where x is in seconds

rate of hot tap = 1/(x+100)
combined rate = 1/x + 1/(x+100)
= (x+100 + x)/(x(x+100))
= (2x+100)/(x(x+100))

time at combined rate = 1/(2x+100)/(x(x+100))
= x(x+100)/(2x+100)
but we know this is 360 seconds

x(x+100)/(2x+100) = 360
x^2 + 100x = 720x + 36000
x^2 - 620x - 36000 = 0
x = 673.46 seconds or a negative
(I used the quadratic formula)

using the cold tap alone would take appr 673.5 seconds or
11 minutes and 13 seconds

check:
rate of cold = 1/673.5
rate of hot = 1/773.5
comined rate = sum of those two = appr .0027777...
time at comined rate = 1/.002777..
= 360 seconds
or 6 minutes

To find out how long it would take the cold tap on its own to fill the bath, we need to determine the time it takes for the hot tap alone and the difference between the hot and cold taps.

Let's start by finding the time it takes for the hot tap alone:

If it takes the old and hot tap 6 minutes to fill the bath, we know that the hot tap contributes to the entire process. Therefore, we can assume that the hot tap on its own takes 6 minutes.

Next, we need to determine the difference in time between the hot and cold taps:

We are given that the hot tap takes 100 seconds (secs) longer than the cold tap to fill the bath. Since 1 minute is equal to 60 seconds, 100 seconds is equivalent to 100/60 = 1.67 minutes.

Now, we can subtract the difference between the hot and cold taps from the total time it takes for the hot tap:

6 minutes - 1.67 minutes = 4.33 minutes

Therefore, it would take the cold tap on its own approximately 4.33 minutes to fill the bath.