3.4 Processing data 91
Commentary
This question has a lot of data presented
verbally. We must identify the important
variables to calculate in order to answer the
question. This is done by working backwards:
we need the number of weeks the water in the
butt will last. This, in turn, depends on the
amount of water in the butt at the start
(already known) and the average loss of water
per week. The average loss of water per week is
the amount collected minus the amount used
(which we also know). Thus, the only
unknown is the amount collected. This is
what we need to calculate first.
The weekly rainfall is 5 mm, which is
collected on an area of 6 m^2. In consistent
units (using metres) the volume collected is
6 m^2 × 0.005 m of rain or 0.03 cubic metres. A
cubic metre is 1000 litres, so the volume
collected is 30 litres.
As Cheng uses 60 litres per week and
collects 30 litres, he loses a net 30 litres each
week. Thus his 200-litre butt will last for 5
weeks; at the beginning of the sixth he will
have only 50 litres, which is not enough to top
up his pond.
This question illustrates one method of
approaching problem-solving questions. We
know what answer is required, so which pieces
of information do we need to come up with to
get that answer? This indicates which
calculations need to be made on the given
data. It may be represented as shown on the
following page.If you are worried about remembering these,
there is an easy way. Speed is measured in
units such as km/h or m/s. This is a
distance divided by a time, which is
equivalent to the first formula – the others
can be worked out from it.
Always check that you use consistent
units in calculations. If the speed is in
metres per second and the time is given in
minutes, you must first convert the time to
seconds (or the speed to metres per
minute) before applying the formula.
Also, consider whether your final answer
is a reasonable number. If, in the example
given above, you had divided Bianca’s
distance in km by the speed in m/s you
would have an answer of 1.5 ÷ 5 = 0.3. A
value of 0.3 seconds or minutes would
clearly be ridiculous for cycling 1.5 km (and
hours did not appear in the calculation) so it
is obvious that something is wrong.
Care must be taken when calculating
average speeds. Say, for example, that a
river ferry travels between two towns 12 km
apart, travelling at 4 km/h upstream and
6 km/h downstream. It might seem that the
average speed will be 5 km/h, but this is
wrong. In order to calculate the average
speed, you must divide the total distance
by the total time. In this case, the ferry
takes 3 hours upstream and 2 hours
downstream – a total of 5 hours. The
average speed is, therefore, 24 ÷ 5 or
4.8 km/h.Cheng has a garden pond, which he tops up
at the beginning of each week from a
200-litre water butt, which is, in turn, filled by
rainwater from part of his roof. At the
beginning of the summer both the pond andActivity
the water butt are full. The average weekly
summer rainfall where he lives is 5 mm. The
part of his roof from which he collects rain
has an area of 6 m^2. He uses 60 litres per
week on average to top up the pond.
For how many weeks can Cheng expect to
have enough water in the butt to top up the
pond fully?