## Quadratic Equations

## Exercise 4.3

Two water taps together can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank??

Let the time taken by larger tap (A )= x hours

Time taken by smaller tapÂ (B)= (x-10) h

Time taken by both taps (A+B)= 9and 3/8 hours = 75/8 h

According to the question

A’s one hour work+ B’s one hour work = (A+B)’s one hour work

1/x+ 1/(x-10) = 8/75

Taking LCM, and cross multiplying

75(2x-10) = 8( xÂ²- 10x)

150x – 750 = 8xÂ² – 80x

75x – 375 = 4xÂ² – 40x ( dividing by 2)

4xÂ² -115x +375 = 0

4xÂ²- 100x-15x+375= 0

(4x-15)(x-25)= 0

âˆ´ x= 15/4 and x= 25

Value of x can’t be 15/4(3.75) because the other tap takes 10h less than this which is not possible

âˆ´ larger tap takes 25 h

And smaller takes 15 h