Question

two water tops together can fill a tank in 6 hours. the tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. find the time in which each tap can take separately fill the tank​

Answer 1

Answer:

Let 'v' m

3

be the volume,

(x+y)→6 hours

x→k hours

y→(k−9) hours

Rate of x⇒

k

v

m

3

/hr

Rate of y⇒

(k−9)

v

m

3

/hr

Rate of (x+y)⇒

6

v

m

3

/hr

∴

k

v

+

k−9

v

=

6

v

⇒

k

1

+

k−9

1

=

6

1

6(k−9+k)=k(k−9)

⇒6(2k−9)=k

2

−9k

⇒12k−54=k

2

−9k

⇒k

2

−21k+54=0

(k−18)(k−2)=0

k=18,3

∴x⇒18 or 3 hours

y⇒9 or −6 hours (Not possible)

∴x=18 hours & y=9 hours.