3.8 Hypotheses, reasons, explanations and inference 109
they leave Whitesea at 9.00 a.m., 9.20 a.m.,
9.40 a.m., etc. They then leave Greylake 1 hour
10 minutes later, at 10.10 a.m., 10.30 a.m.,
10.50 a.m., etc. A driver leaving Whitesea, for
example, at 11.20 a.m. will see the trams which
left Greylake at 10.30 a.m., 10.50 a.m.,
11.10 a.m., 11.30 a.m., 11.50 a.m. and
12.10 p.m. – six in total.
Looking at statement A, the first tram
leaving Whitesea at 9.00 a.m. reaches Greylake
at 10.00, leaves at 10.10 and returns to
Whitesea at 11.10, in time to become the 11.20
service. In the meantime, other trams will
have left at 9.20, 9.40, 10.00, 10.20, 10.40 and
11.00, i.e. six more, so there must be seven
trams to run the service. A is incorrect.
Looking at statement C, if I sit near the
midpoint from 11.15 a.m. to 12.15 p.m., I will see
the 11.00, 11.20 and 11.40 trams going one way
and the 10.50, 11.10 and 11.30 trams going the
other way, so I will see six in total. C is correct.
Can you confirm these answers by
constructing a timetable?
This kind of problem will be revisited in
Chapter 6.2 where we look at graphical
solutions to problems.• We have encountered examples where we
are required to suggest a hypothesis or a
reason for the nature of variation in data.
• The terms hypothesis, reason, explanation
and inference are used in exactly the
same way in problem solving as in critical
thinking, the only difference being that the
information given is in the form of data
rather than verbal description.
• We have seen that extended examples
where more data is supplied can require
analysis that may lead to a range of
conclusions.Summary
Commentary
We can test the statements by making a
timetable. However, to do this, we need to make
an assumption about the departure intervals. It
is, in fact, better to carry out a little analysis first.
When a tram driver leaves Whitesea, all
those trams which left Greylake up to one
hour earlier will already be on their journey.
During the hour it takes him to travel to
Greylake, more trams will be leaving Greylake.
So, in total, he will see all those trams which
left up to an hour before he left, and also all
those which leave up to an hour after he left.
This means the six trams he sees must have left
Greylake in a two-hour period. As they leave at
regular intervals, one must leave every
20 minutes, so B is incorrect.
This may be illustrated by looking at some
actual times. If trams leave every 20 minutes,
(Harder task) A tram company runs a service
along the seafront from Whitesea to Greylake.
Trams leave Whitesea at regular intervals,
starting from 9 a.m., taking one hour to reach
Greylake. They then turn around and start
back 10 minutes after arriving. A driver in the
middle of the day, in his journey from Whitesea
to Greylake, always sees six trams travelling in
the opposite direction. Some of these will
have set off from Greylake before he left, and
some will have set off after he left.
Which of the following must be true? There
may be more than one. If any of the
statements are not true, can you correct
them?A It takes six trams to run the service.
B The trams run every ten minutes.
C If I sit on the seafront from 11.15 a.m.
to 12.15 p.m., I will see six trams
going past.Activity