Question

Two pipes together can fill the tank in 6 hours 20 minutes.one tap takes 3 hours more than the other to fill the tank separately.find the time in which each tap can separately fill the tank.

Answer 1

Answer:

let time taken by 1 tank be x

then time take by other will be x+3

1/× + 1/×+3 =19/3

3(2×+3)=19(×^2 +3×)

Step-by-step explanation:

now the eqn can be solved simultaneously...

Answer 2

Time take by first pipe = 12 hours

Time taken by second pipe = 15 hours.

Explanation:

Let the time taken (in hours) by one tap to fill tank alone be 'x' and the time taken by the second tap be 'x+3'.

Given : Time taken by both pipes to fill tank together = 6 hours 20 minutes

$=6+\dfrac{20}{30}$ hours

= $6+\dfrac{2}{3}\text{ hours }=\dfrac{20}{3}\text{ hours}$

According to the question ,

$\dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{1}{\dfrac{20}{3}}\\\\\Rightarrow\ \dfrac{x+3+x}{x(x+3)}=\dfrac{3}{20}\\\\\Rightarrow\ 20(2x+3)=3(x^2+3x)\\\\\Rightarrow\ 40x+60=3x^2+9x\\\\\Rightarrow\ 3x^2-31x-60=0$

using quadratic formula : $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{31\pm\sqrt{(31)^2-4(3)(-60)}}{2(3)}=\dfrac{31\pm \sqrt{1681}}{6}\\\\ \x=\dfrac{31\pm 41}{6}\\\\ x=\dfrac{31+41}{6}=12; x=\dfrac{31-41}{6}=-1.667$

Since time cannot be negative , then x= 12

Thus , the time take by first pipe = 12 hours

Time taken by second pipe = 15 hours.

# Learn more :

Two taps running together can fill a tank in 6 hours. If one tap takes 5 hours more than the other to fill the tank, find the time in which each tap would fill the tank.

https://brainly.in/question/11254880