Question

The water dam is filled up using the first tributary in 1 hour and 10 minutes, using the second tributary in 60 minutes. How many minutes it takes to fill the half of the dam using both of the tributaries, if the second tributary will be opened 12 minutes after the first one?

Answer 1

Answer:

Let the time taken by the larger tap alone to fill the tank be x minutes.

∴ Tank filled in 1 minute =

time taken by smaller tap to fill the tank alone = x + 10.

∴ Tank filled in 1 minute =

time taken by both of the taps to fill the tank = 12 minute.

Now in 1 minute they both will fill th of the tank.

⇒

⇒ (2x + 10)12 = x2 + 10x

⇒ x2 + 10x – 24x – 120 = 0

⇒ x2 – 14x – 120 = 0

⇒ (x–20)(x + 6)

time cannot be negative so 20 minutes for larger tap

and 30 minutes for smaller tap.