Question

A tank of 425 litres capacity has been filled with water through two pipes, the
first pipe having been opened five hours longer than the second. If the first pipe
were open as long as the second, and the second pipe was open as long as the
first pipe was open, then the first pipe would deliver half the amount of water
delivered by the second pipe

Answer 1

Answer:

Step-by-step explanation:

given  

A tank of 425 litres capacity has been filled with water through two pipes, the  first pipe having been opened five hours longer than the second. If the first pipe  were open as long as the second, and the second pipe was open as long as the  first pipe was open, then the first pipe would deliver half the amount of water  delivered by the second pipe; if the two pipes were open simultaneously, the  tank would be filled up in 17 hours. How long was the second pipe open?

We know that work = e x t

So work = 425 and time = 17

Efficiency = w/t

             = 425 / 17  

              = 25

So efficiency of first and second pipe will be 25

According to question first pipe is opened 5 hours longer than the second , so it will be x – 5, x

So x – 5 + x = 25

2x = 30

x = 15

Now first pipe will be 15 – 5 = 10 hours   and

second pipe will be for 15   hours

Answer 2

Total eff (A+B)=425/17=25

A(t+5)+Bt=425

t(A+B)+5A=425

25t+5A=425

5t+A=85

A=85-5t (i)

B=25-A =5t-60 (ii)

And also 2At=Bt+5B

After solving these equations

3t²-41t-60=0

(3t+4)(t-15)=0

t=15(only positive value)