Question

Two taps together can fill a tank in 15/8 hours . the tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
(Class 10 Quadratic Equations)

Answer 1

Answer:

let tap with smaller diameter takes x hrs

tap with larger diameter takes x - 2 hrs

both tap will fill tank in 1 hr = 8/15

both tap will fill tank in 1 hr = 1/x + 1/x-2

A.T.Q.

1/x + 1/x-2 = 8/15

x -2+x / x(x-2) = 8/15

2x -2 / x2 -2x = 8/15

8( x2 -2x ) = 15(2x -2)

8x2 - 16x = 30x -30

8x2 - 16x -30x +30 =0

8x2 - 46x +30 = 0

Answer 2

Time taken by shorter tap = 5 hours

Time taken by longer tap = 3 hours

Step-by-step explanation:

Let the time taken by the smaller tap be 'x'.

Let the time taken by the longer tap be 'x-2'.

Total time = $\dfrac{15}{8}\ hours$

According to question, it becomes,

$\dfrac{1}{x}+\dfrac{1}{x-2}=\dfrac{8}{15}\\\\\dfrac{x-2+x}{x(x-2)}=\dfrac{8}{15}\\\\\dfrac{2x-2}{x^2-2x}=\dfrac{8}{15}\\\\15(2x-2)=8(x^2-2x)\\\\30x-30=8x^2-16x\\\\8x^2-16x-30x+30=0\\\\8x^2-46x+30=0\\\\x=0.5,5$

So, we will select 5 hours as the value of x because if we take 0.5 it will give us negative value for longer tap.

So, Time taken by shorter tap = 5 hours

Time taken by longer tap = 5-2 = 3 hours

# learn more:

Two water taps together can fill a tank in 15 by 8 hours .the tap with longer diameter takes 2 hours less than the smaller one to fill the tank separately .find the time in which each tap can fill the tank separately

https://brainly.in/question/8621988