Question

Rational function

Answer 1

Pomp a can make a pool empty in 10 hour, pomp b in 15 hour. How long will it take to empty the pool if both pomps are working?

Answer 2

@electrokid

Answer 3

you mean "pump" lol

Answer 4

Sorry, I had too translate

Answer 5

total volume to pump = V (say)

Answer 6

the rate of pumping are:
\[r_a={V\over10}\qquad r_b={V\over 15}\\
r=r_a+r_b=V\left({1\over10}+{1\over15}\right)=?\]

Answer 7

r = combined rate of pumping

Answer 8

get it?

Answer 9

No.

Answer 10

which part?

Answer 11

we are not done with the answer. you find the "?"

Answer 12

my book says it's 6 hours

Answer 13

\[r={V\over ?}\]

Answer 14

I am guiding you to the answer

Answer 15

I don't understand, can you start again with the very beginning?

Answer 16

whaat
ok
total voume of water to pump = V

Answer 17

Yes

Answer 18

and? @electrokid

Answer 19

ok
then,
rate of pump = volume pumped / time taken
(this is like speed of a car = distance / time)

Answer 20

good?

Answer 21

Why do you need rate, you already know 15 and 10 hours?

Answer 22

yes from that you calculate at what rate each pump pumps the water out

Answer 23

when you combine them, what changes?
rate at which water is pumped = rate of pumping water by both the pumps

Answer 24

yes, the rate changes.

Answer 25

good
that is whywe calculate the rates

Answer 26

how do I know the volume?

Answer 27

we do not..
lets keep it at V

Answer 28

ok

Answer 29

so we get the above rates and add them
\[r = {V\over10}+{V\over15}={15V+10V\over15\times10}={V\over 6}\]

Answer 30

what does this tell you?
this says that the combined rate takes 6hrs to pump the "V" amount