There are two pipes in a water reservoir of our school. Two pipes together take
11¹/9 minutes of fill the reservoir. If the two pipes are opened separately, then one pipe would take 5 minutes more time than the other pipe. Let us write by calculating, the time taken to fill the reservoir separately by each of the pipes.
Answers
Answer:
Given :-
- There are two pipes in a water reservoir of our school. Two pipes together take 11¹/9 minutes of fill the reservoir. If the two pipes are opened separately, then one pipe would take 5 minutes more time than the other pipe.
Find out :-
- The time taken to fill the reservoir separately by each of the pipes.
Solution :-
Suppose time taken to fill by first is x minutes
So,
Time taken to fill by 2nd is (x + 5) minutes.
★ In minutes filled by the 1st = 1/x part
★ In 1 minutes filled by the 2nd is 1/x + 5 part
★ By two filled in 1 minutes (1/x + 1/x + 5) part
➻ x + 5 + x/x(x + 5) part
➻ 2x + 5/x(x + 5) part
★ 11¹/9 minutes
➻ 100/9 minutes filled = (2x + 5) × 100/x(x + 5) × 9 part
So,
★ (2x + 5) × 100/x(x + 5) × 9 = 1
➻ 9x(x + 5) = 100(2x + 5)
➻ 9x² + 45x = 200x - 500
➻ 9x² + 45x - 200x - 500 = 0
➻ 9x² - 155x - 500 = 0
➻ 9x² - 180x + 25x - 500 = 0
➻ 9x(x - 20) + 25(x - 20) = 0
➻ (x - 20) (9x + 25) = 0
➻ (x - 20) = 0
➻ x - 20 = 0
➻ x = 20
Either,
➻ (9x + 25) = 0
➻ 9x + 25 = 0
➻ 9x = - 25
➻ x = - 25/9
➪ x = - 25/9 because time is not negative
➪ x = 20
★ Time taken by the first is 20 minutes and that by the 2nd is (20 + 5) minutes
➔ 25 minutes
∴ Time taken by the first is 20 minutes.
Time taken by the second is 25 minutes.