Pipe A can fill a pool in 15 minutes and pipe B alone can do it in 10 mibutes. Both the pipe are opened after 4 minutes water from pipe B stop flowing.In how much time will pipe A fill the part of the pool

let 1= total job

rate=job/min
for A=the rate is 1/15
for B= the rate is 1/10
at 4 minutes both were open..so the part of the job done is..
(1/15+1/10)X 4min= 2/3
but after 4 min pipe B closed so A has to work alone...then
(1/15)(x)
where x is the time..adding both and equate it to the total work done
2/3 + x/15 = 1
finding for x
x= 5 minutes..

rate of pipe A = 1/15

rate of pipe B = 1/10
combined rate = 1/6

amount done after 4 minutes = 4(1/6) = 2/3
so 1/3 is left to be done

time using only A
= (2/3) / (1/15)
= 10 minutes

its 5

if 1/3 is left and using a then.

1/3=(1/15)x
x=5

Thanks nms for catching my error

I used 2/3 instead of 1/3

(I must have looked back at the wrong fraction)

To find out how long it will take for Pipe A to fill the remaining part of the pool after Pipe B stops flowing, we can calculate the rate at which each pipe fills the pool.

Let's denote the rate at which Pipe A fills the pool as "x" (in pool per minute) and Pipe B as "y" (in pool per minute).

From the information given, we know that:
Pipe A can fill the pool in 15 minutes, which means its rate is 1/15 pool per minute (x = 1/15).
Pipe B can fill the pool in 10 minutes, which means its rate is 1/10 pool per minute (y = 1/10).

Both pipes are opened after 4 minutes, so in those 4 minutes, Pipe B has already filled a part of the pool. We need to find out what fraction of the pool Pipe B fills in 4 minutes.

Pipe B's rate is 1/10 pool per minute, so in 4 minutes, it would fill:
4 * (1/10) = 4/10 = 2/5 of the pool.

Now, we subtract the part filled by Pipe B from the total pool:
1 - 2/5 = 3/5 of the pool remains to be filled.

Since Pipe A is the only pipe filling the remaining part of the pool, we need to find out how long Pipe A takes to fill 3/5 of the pool.

Pipe A's rate is 1/15 pool per minute, so the time it takes to fill 3/5 of the pool is:
(3/5) / (1/15) = (3/5) * (15/1) = 3 * 3 = 9 minutes.

Therefore, Pipe A will take 9 minutes to fill the remaining part of the pool after Pipe B stops flowing.