A swimming pool can be filled by two pipes together in 6 hours. If the larger pipe alone takes 5 hours less than the smaller pipe to fill the pool, find the time in which each pipe alone would fill the pool?
Answers
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:
Larger Pipe = 10 hours
Smaller pipe = 15 hours
Step-by-step explanation:
Let the time taken by the larger pipe be x
The time take by the smaller pipe = x + 5
Solve x:
Given that the time needed is 6 hours
1/x + 1/(x + 5) = 1/6
(x + 5 + x) / x(x + 5) = 1/6
(2x + 5)/x(x + 5) = 1/6
6(2x + 5) = x(x + 5)
12x + 30 = x² + 5x
x² - 7x - 30 = 0
(x - 10) (x + 3) = 0
x = 10 or x = -3 (rejected, since time cannot be negative)
Find the time needed for each pipe:
Larger pipe = x = 10 hours
Smaller pipe = x + 5 = 10 + 5 = 15 hours
Answer: Larger pipe takes 10 hours and the smaller pipe takes 15 hours