A rectangular tank can be filled with water by two pipes in

A rectangular tank can be filled with water by two pipes in 100/9 minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the...

smaller pipe, find the time each pipe takes to fill the tank.

Solution

In accordance with the data, we assume the larger of the pipe alone takes x+5 minutes to fill up the water tank and the smaller alone in x minutes.

So, the fraction of the tank filled by the larger pipe in 1 minute is 1/(x+5), and the fraction of tank filled by the smaller pipe in one munute = 1/x.

So the fraction of the tank filled by the two pipes together in one minute =1/(x+5)+1/x =(2x+5)/[x(x+5)]

Therefore, the number of minutes required by them to fill algebraically = 1/ {(2x+5)/[x(x+5)]}= x(x+5)/(2x+5) but this is said to be equal to 100/9 minutes by the data.

Therefore, x(x+5)/(2x+5)=100/9 .

Multiply by the LCM of the denominators both sides:

9x(x+5)=100(2x+5)

9x^2+45x=200x+500

9x^2+45x-200x-500=0

9x^2-180x+25x-500=0

9x(x-20)+25(x-20)=0

(9x+25)(x-20)=0

x=20 and x+5=25

Therefore the time taken by the larger and smaller pipes individully to fill up the water tank : 20 and 25 minutes respectively.

Hope this helps.