Question

This is for maths aryabhattas..
⏬⏬


There are two taps. A tank fills completely in 2 hours if the both taps are open. If only one of the tap is open at a given time, the smaller tap takes 3 hours more than the larger tap to fill the tank. How much time do each tap take to fill the tank completely?


thanks...​

Answer 1

for my brother

let's do it

ok

let the time taken by smaller tap be x hours

then by larger tap be x-3 hours

so

the larger tap will do

1/x-3 work in 1 hour

and the smaller tap will do 1/x

so they both will do

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

2x-3/x^2-3x=1/2

4x-6=x^2-3x

x^2-7x+6=0

x^2-6x-x+6=0

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

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

so

x=6

and x=1

but x can't be 1 because then x-3 will be negative which is not possible

so

time taken by smaller tap=6

time taken by larger tap=6-3=3

thanks for asking

today no rap if you want I can

Answer 2

$\huge{HELO-MATE}$ ✌
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

$Solution$ => 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.

❤☺____________________☺❤

$<marquee > Hope it's help uhh$ ✌


mark my answer as brainlist.....❤