Question

Two pipes together can fill a tank in 20/3 hours if the pipe of smaller diameter takes 3 hours more than the pipe of larger diameter to fill the tank separately find the time taken by each pipe to fill the tank separately

Answer 1

Answer :

Let,

A pipe of big diameter is Y, and another smaller diameter pipe is X

According to the question,

Two pipes fill a tank together in 20/3 hours

So,

X + Y  =20/3   ..........(1)

The pipes of small diameter take more 3 hours  more than small diameter of pipe

There for X = Y + 3

                X - Y = 3 ...........(2)

sum of equation (1) and (2)

X + Y =   20/3.....(1)

X - Y =   3..........(2)

2X   = 20/3 +3

2X  = 29/3

X  = 29/ 6  hours  

Put the value of X in to equation (1)

29/ 6 + Y  = 20/ 3

Y  = 20/ 3 - 29/ 6

Y  = 11/ 6 hours

It means  pipes of small diameter take time to fill tank = 11/ 6 hours

and pipes of big diameter take time to fill tank = 29/ 6 hours

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Answer 2

Step-by-step explanation:

Given Two pipes together can fill a tank in 20/3 hours . If pipe of smaller diameter takes 3 hours more than the pipe of larger diameter to fill the tank separately, find the time taken by pipe to fill the tank

• Let pipe A and pipe B fill the tank in p hours and p + 3 hours.
• In 1 hour pipe A , 1/p part of the tank will be full
• Also in 1 hour for pipe B, 1/p + 3 part of the tank will be full.
• So it will be 1/p + 1/p+ 3
•     = p + 3 + p / p(p + 3)
•    = 2 p + 3 / p(p + 3)
• Therefore 2p + 3 / p(p + 3) part of the tank will be full in 1 hour
• So 1 full tank will fill in 1 / (2 p + 3) / p(p + 3)
•           = p(p + 3) / 2p + 3

•        Now p(p + 3) / 2p + 3 = 20 / 3
• Or 3p (p + 3) = 40 p + 60
• Or 3p^2 – 31 p – 60 = 0
• Now p = - b + - √b^2 – 4ac / 2a
•          = - (- 31) + - √(-31)^2 + - 4 (3)(-60) / 2(3)
•         = 31 + - √961 + 720 / 6
•      = 31 + - √1681 / 6
•       = 31 + - 41 / 6
•            = 72 / 6 or  - 10 / 6
•             = 12 hours

So the time taken by the pipe to fill the  tank will be 12 hours.

Reference link will be

https://brainly.in/question/8460317