Question

A 100-litre tank filled with water is leaking water at the rate of 2.5 litres per hour.

a) How long will it take for the tank to be half full?

Once it is half full, water is added to the tank at the rate of 3 litres per hour.

b) How much longer will it take until the tank is full again?

Answer 1

I've done and got part a correct correct already. I need help with part b.

Answer 2

for it to be full it needs 50 litres...since it was half right

Answer 3

so just do 50/3

Answer 4

no but it is still leaking 2.5L per hour

Answer 5

ohh well that's different

Answer 6

so yes we need 50L more to be filled back to 100L(the starting point)

Answer 7

and although we are adding 3L per hour 2.5L is still leaking per hour so only 0.5L is actually added.

Answer 8

so it's like 0.5 litres is just added per hour

Answer 9

however if you do 50/0.5 you wont get the right answer

Answer 10

yep, that's why I need help.

Answer 11

im thinking you neeed to do 50/0.5 THEN divide by 2

Answer 12

because by dividing by 2 you're going to see when it first got full....my hypothesis only though

Answer 13

leakage at a rate of 2.5 l/ hr..

so for 50 liters = 50/2.5 = 20 hrs..

Now to full the tank again to 100 liters,

50/2.5 + 50/ 3 = 36.67 hrs ... what say guys ??

Answer 14

nope.

Answer 15

The answer is actually 100hours for part b but I do not know how it is achieved.

Answer 16

actually I got it.

Answer 17

100? 50/0.5???

Answer 18

yeh

Answer 19

sorry i missed a step...

leakage at a rate of 2.5 l/ hr..
so for 50 liters = 50/2.5 = 20 hrs..

so 1/2 tank is emptied in = 1/20 hrs..

Now, time taken to fill 50liters at a rate of 3 l/hr.. = 50/3 = 16.67 hrs..

So, 1/2 tank is filled in = 1/16.67 hrs..

Now when both happens together, = (1/16.67) - (1/20) = 3.33/ (20 * 16.67) = 1/100.12..

so tank will be filled in 100.12 hrs...

Answer 20

that's wrong o.O well it's partially right...but that's not when it will reach full tank

Answer 21

50/0.5 = 100
I believed I did 50 x 0.5 = 25 so I must have got it wrong by accidentally pressing the x and not the divide sign.

Answer 22

i agree that in 100 hours the tank will reach fulll...but the tank will reach full before 100 hours too

Answer 23

how?

Answer 24

@lgbasallote : actually little more than 100 hrs... i have calculated that..

Answer 25

hmmm

Answer 26

nevermind...it's happening simultaneously

Answer 27

@Ganpat, ur method is too complicated for my likes sorry.

Answer 28

and although ur method seems to work the answer I've got of exactly 100 seems to be more correct.

Answer 29

you can use
distance = time * (effective speed)

Answer 30

@JayDS : 50/0.5 , might be the right answer ion this case.. but it may not be true for different problems...

Answer 31

here,
distance is related to - water accumalted
speed is related to - flow rate

Answer 32

lol but there's no distance here....

Answer 33

@JayDS : Its not actually.. its a trick to solve this leakage problems..

always convert them into per unit... calculations will be easy... and it always works..

Answer 34

and we do not need to find distance.

Answer 35

ok, I'm not sure if it works using @ganeshie8's way but thanks.

Answer 36

it works.
its a generic relation. it works for any speed/distance/rate situations

Answer 37

okok, it seems to relate to Physics which I do not learn lol, so I rather keep it simple as possible.

Answer 38

its not physics. its just a relation. forget about the terminology i used if it confuses

Answer 39

and @ganpat I'll give u the medal since u tried so hard and to help me, u troll. lol

Answer 40

ha ha, ..
@JayDS:
but its a really good, simple and prominent method.. SO try to grasp it.. i can help u understand...

Answer 41

yes..
and,

if the relation quoted above seems new, here is another way :

1) amount of water coming into tank = 3*t
2) amount of water leaving out of tank = 2.5*t
3) amount of water in tank = 3t-2.5t


50 = 3t-2.5t

50 = .5t

t = 100