Rational expression word problem please help

suppose you are running water into a tub. the tub can be filled in 2 min if only the cold tap is used. it fills in 3 min if only the hot tap is turned on. how long will it take to fill the tub if both taps are on simultaneously.

thanks

let x = volume

cold*2 = x cold = discharge from cold tap

cold = x/2

hot*3 = x hot = discharge from hot tap

hot = x/3

cold*y + hot*y = x

xy/2 + xy/3 = x

y/2 + y/3 = 1

3y/6 + 2y/6 = 1

y = 6/5 = 1.2 min = 72 seconds

Let V be the volume of the tub and C and H be the amount of cold and hot water coming out per min respectively.
then V = 2C = 3H
Now let T be the time taken to fill the tub with both taps open
then V=T(C+H) = T(3H/2+H) = T(5H/2) = T(5/2)*V/3 = TV5/6
Cancelling V on both sides we get T= 6/5 min = 72 seconds

c = 1/2
h = 1/3
b = c+h = 1/2+1/3 = (3+2)/6 = 5/6

The fill rate if both taps are used is 5/6 tub/minute or 6 minutes to fill 5 tubs or 1.2 minutes to fill the tub.

Answer: 1.2 minutes or 1 minute 12 seconds.

Cold water fills the tub at 0.5 tubs per minute

Hot water fills the tub at 0.33 tubs per minute.

0.5 + 0.33 = 0.83 tubs per miute. 1 tub /.83 tubs per minute = 1.20 minutes.

Alot