Question

Tap A can empty a tank in 6 hours. Tap A along with Tap B together can empty the tank in `3(3)/(7)" hours"`. Find the time Tap B alone will take to empty the tank.

Answer 1

Time taken bt Tap A to empty the tank = 6 hours

Amount of work done by tap A in 1 hour = `(1)/(6)`

Let B takes x hour to empty the tank alone.

Amount of work done by tap B in 1 hour = `(1)/x`

∴ Amount of work done by (A + b) in 1 hour = `(1)/x + (1)/(6)`

Tap A along with Tap B together can empty the tank in `3(3)/(7)" hours" = (24)/(7)" hours"`

∴ In 1 hour amount of work done by A and B = `(1)/((24)/(7)) = (7)/(24)`

Now, according to the question

`(1)/x + (1)/(6) = (7)/(24)`

⇒ `(1)/x = (7)/(24) - (1)/(6)`

= `(7 - 4)/(24)`

= `(3)/(24)`

= `(1)/(8)`
⇒ x = 8hrs.