Question

a rectangular tank can be filled with water by two pipes in 100/9 minutes.If the large pipe alone takes 5 minutes less to fill the tank than the smaller pipe finde the time each pipe takes to fill the tank

Answer 1

Let,the time taken by larger pipe = x
By smaller pipe = x+5

It would be: 1/x + 1/(x+5) = 9/100
= x+5+x /(x)(x+5) = 9/100
= 2x+5 / x²+5x = 9/100
= 100(2x + 5) = 9(x² + 5x)
= 200x + 500 = 9x² + 45x
= 9x² - 155x - 500 = 0
= 9x² - 180x + 25x - 500 = 0
= 9x(x - 20) + 25(x - 20) = 0
= (9x + 25) (x - 20) = 0
= x = -25/9 or x = 20

Time can't be in negative so -25/9 is rejected.
Now,x + 5 = 20 + 5 = 25

In short, Your Larger pipe takes 20 minutes and smaller pipe takes 25 minutes

Hope this helps!