Question

Q. 9, Two water taps together can fill a tank in 9 hours 36
minutes. The tap of larger diameter takes 8 hours
less than the smaller one to fill the tank. Find
the time in which each tap can separately fill the
tank.​

Answer 1

Let the time taken by the tap of smaller diameter be x hours.
So, time taken by the tap of larger diameter be (x - 8) hours
Work done by the tap of smaller diameter in one hour is 1/x
So, time taken by the tap of larger diameter in one hour is 1(x - 8)

The work done by the 2 taps together in 1 hour 1/x + 1/(x - 8)
According to the question,
1/x + 1/(x - 8) = 5/48
Solving this we get
5x2 - 136x + 384 = 0
x = 24 as x = 16/5 rejected
The time taken by the tap of smaller diameter be 24 hours.

Answer 2

Answer:

Step-by-step explanation:

Let the time taken by the tap of smaller diameter = x years

Therefore time taken by the tap of larger diameter = ( x - 8 ) hours

Work done by the tap of smaller diameter in one hour = 1÷ x

and the work done by the tap of larger diameter in one hour = 1 / x - 8

Thus , the work done by the 2 taps together in 1 hour

= 1/x + 1/ x- 8

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

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

The 2 tapes together can fill the tank in x( x- 8)/ 2x - 8 ( reciprocal )

According to question

x( x- 8)÷ 2x - 8 = 36 hrs 19 mins

2x-8/x²-8x =5/48

48(2x-8)=5(x²-8x)

96x-384=5x²-40x

0=5x²-40x-96x-384

=5x²-136x+384

compare with ax²+ bx+c=0

a=5,b=-136,c=384

by quaratic formula

x=-b+-√b²-4ac/2a

=-(-136)+-√(136)²-4(5)(382)/2(5)

=136+-√18496-7680/10

=136+-√10816/10

=136+-104/10

=+ve 136+104/10

=240/10

=24

-be 136-104/10

= 32/10

=16/5

X = 24 as it can not be 16/5

Thus time by smaller pipe= 24 hrs

Time by larger pipe = 24-8 = 16 hrs

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