Question

Tap A can fill an empty tank in 6-hours and Tap B can empty the full tank in 8-hours. If
the tank is empty when tap A is opened at 9:00 am and tap B is opened at 11:00 am,
then at what time is the tank filled

Answer 1

In 1 hour

Tap A = 1/6 ( of the work) in 1 hour

Tap B = -1/8 (of the work)

Now lets Assume

Tap B is opened for x hours

Tap A is opened 2 hours earlier; 

Hence tap A is opened for x + 2 hours
1/6( x+2)  - 1/8 x = x
x/6 + 1/3 - x/8  = x

(4x - 3x - 24 x )/24    = -1/3
 -23x/24  = -1/3

x = 1/3 * 24/23  = 8/23approx 20 mins

Time it is filled

11: 20