Maths problem

Guest1 · Post by **Guest1** » Thu Dec 27, 2007 4:53 pm

Can anyone help with the following question from the 2004 Habs Boys Maths paper:

A water tank is a cuboid with width 60cm, length 100cm and height 100cm.
a. Find the area of the base of the tank in square centimetres.
b. Use the fact that there are 1000 cubic centimetres in a litre to write down the volume of the tank in litres.
c. Initially the tank is half-full. Water is poured into the top of the tank at a constant rate of 30 litres per minute. How long will it take before the tank is three-quarters full?
d. At this point the tank springs a leak so that water pours out of the bottom at a constant rate of 15 litres per minute. If the water continues to be poured into the top at the same rate as before, how much longer will it be before the tank is full?

A worried mum.

Wallasey · Post by **Wallasey** » Thu Dec 27, 2007 8:25 pm

I think this is right...

a. area of base = l x w which is 60 x 100 = 6000cm2

b. volume = l x w x h which is 6000 x 100 = 600000cm2
then divide by 1000 to turn into litres = 600 litres.

c. 300 litres initially, rising to 450 litres is 150 litres to add.
At 30 litres per min this would take 150/30 = 5 mins.

d. Now the rate is halved to 30- 15 litres per min, i.e. 15 litres per min.
At 15 litres per min this would take 150/15 = 10 mins.

Hope it's helpful (and correct!)

Guest1 · Post by **Guest1** » Thu Dec 27, 2007 9:24 pm

Hi Wallasey,

Many thanks for your clear and concise explanation.

Not so worried mum.

Guest · Post by **Guest** » Thu Dec 27, 2007 10:17 pm

Habs Maths 2004 is one of the papers we do not have in our Habs collection. So, I gave my son the question to solve, with the assurance that I did not have to work it all out as Wallasey had posted the answers!
My son solved the first 3 and wasn't too sure about the wording of the last one , but eventually understood it.
Please keep us posted with any others.