Bath Time : You have left the plug in the bath and you are filling the bath with both taps on.?

Question

The hot tap takes 6 minutes to fill the bath.
The cold tap takes 4 minutes to fill the bath.
The bath empties in 12 minutes (assume uniform rate).
In how many minutes will the bath be filled?

Answer 1

1/6*t+1/4*t-1/12*t=1 multiply both sides by 12 (lcm)
2t+3t-t=12
4t=12
t=3 minutes to fill. This is if the plug is left out.
If the plug is in: 1/6t+1/4t=1 multiply by 12 again
2t+3t=12
5t=12
t=12/5=2.4 minutes to fill.