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

Answer 1

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