Two pipes working together can fill a tank in 35 minutes. If the larger pipe alone can fill the tank in 24 minutes less than the time taken by the Smaller pipe, then find the time taken by each pipe working alone to fill the tank.
Answers
Answer:
Time taken by the smaller pipe is 84 minutes and the bigger pipe is 60 minutes.
Step-by-step explanation:
Time taken by the smaller pipe to fill = x min
Time taken by the larger pipe to fill = (x - 24) min
Let us take the reciprocals of them, i.e.,
1/x + 1/x-24 = 1/35
x-24 + x / x² - 24x = 1/35
(2x-24)35 = x² - 24x
70x - 840 = x² - 24x
x² - 24x - 70x +840 = 0
x² - 94x + 840 = 0
x² - 84x - 10x +840 = 0
x(x - 84) - 10(x - 84) = 0
(x - 84) (x - 10) = 0
x - 84 = 0 x - 10 = 0
x = 84 x = 10
So there are two possibilities,
In first case, x = 84, then,
Time taken by the smaller one to fill = 84 minutes
Time taken by the bigger one to fill = 84 - 24 = 60 minutes
In the second case, x = 10, then,
Time taken by the smaller one to fill = 10 minutes
Time taken by the larger one to fill = 10 - 24 = -14 minutes
The second case is impossible as time can never be in negative.
So, the correct answer is the first case.
Hope its helpful!!!