Question

A swimming pool near a gymnasium is to be filled using hosepipes. A hosepipe P1, delivers 220 gallons of water an hour while another hosepipe P2 delivers 300 gallons of water an hour If the pipe P1, takes 16.5 hours alone to fill up the pool, then the time taken by the pipe P2, operating alone will be

Answer 1

Answer:

10 hours, 15 hours

Step-by-step explanation:

Let the time taken by larger pipe be 'x'.

Then the time taken by the smaller pipe is x + 5.

Given that it can be filled in 6 hours.

⇒ (6/x + 5) + (6/x) = 1

⇒ 6x + 6(x + 5) = x(x + 5)

⇒ 6x + 6x + 30 = x² + 5x

⇒ 12x + 30 = x² + 5x

⇒ x² - 7x - 30 = 0

⇒ x² + 3x - 10x - 30 = 0

⇒ x(x + 3) - 10(x + 3) = 0

⇒ x = -3,10.

⇒ x = 10.

Then:

⇒ x + 5

⇒ 15.

Therefore:

⇒ Time taken by the larger pipe = 10 hours.

⇒ Time taken by the smaller pipe = 15 hours.

Hope this helps!

Answer 2

Answer:

12.1 hours

Step-by-step explanation:

Given that

P1 delivers 220 gallons water/hr

P2 delivers 300 gallons water/hr

P1 takes 16.1 hours alone to fill up the pool

Therefore P1 delivers total of 16.5×220 gallons of water

=3630 gallons of water

Therefore capacity of swimming pool = 3630 gallons of water

Now P2 takes 1hr to deliver 300 gallons of water

Now P2 takes 1hr to deliver 300 gallons of water So, P2 takes 3630/300hr to fill up the pool

Now P2 takes 1hr to deliver 300 gallons of water So, P2 takes 3630/300hr to fill up the pool =12.1 hr