Question

A tank is filled completely in 2 hours if
both taps are open. If only one of the
taps is open at the given time, the smaller
tap takes 3 hrs more than larger to
fill the tank. How much time does
each tap takes to fill the tank completely ?​

Answer 1

Answer:

mark brainlest

Step-by-step explanation:

Let x and y be the respective times in which the tap fills the tank

Now this is work and efficiency question

Before solving this u need to remember that linear operations can be performed only on work done and the rate of doing work

So if a tap is filling a tank in x time then it is doing one work in a designated amount of time

So,

Rate of doing work=(1/x)

Now as per question if both the taps are open then the tank is filled in 2 hours

So

(1/x)+(1/y)=(1/2)

Now it is further stated as

smaller tap alone takes 3 hours more to fill the tank in the same amount

So it can derived that,

(1/x)+(1/(x-3))=(1/2)

Solving this equation ,

(2x+3)/(x^2 -3x)=(1/2)

Rearranging the equation,

x^2-7x+6=0

The following quadratic equation can be solved as,

(x-1)(x-6)=0

x=1,x=6

But x=1 is not possible as x-3 cannot be negative

So

x=6

y=x-3=6-3=3

So the individual time taken by the taps are 3 hours and 6 hours respectively