96 Unit 3 Problem solving: basic skills
questions – that is, checking that we have the
right answer.
If ER takes 24 minutes (including a
3-minute stop) and MR takes 18 minutes (no
stop), then EM (no stop) must take 3 minutes
(24 − 18 − 3). Similarly, RW must take 36 − 18
− 3 = 15 minutes. We now have the times for
all the sections:
EM = 3 minutes
Stop at M = 3 minutes
MR = 18 minutes
Stop at R = 3 minutes
RW = 15 minutes
The total of all these is 3 + 3 + 18 + 3 + 15
= 42 minutes as expected.
Check that the times from E to R and M to
W agree with the answer of 18 minutes from M
to R as given.
This example once again shows that
representing the data in a different way can
lead to a simple method of solving a problem
that at first appears unclear.
Summary
• We have learned the importance of finding
methods of solution for problems for which
the way of proceeding to an answer is not
necessarily obvious.
• We have found that looking for
intermediate results may help to lead to
the final answer.
• We also looked at the value of alternative
ways of presenting data and considering
more than one way of solving problems.
Commentary
A diagram makes this problem much easier to
solve.
42 min
24 min
36 min
EMRW
It can now be seen that if we add the time from
E to R to the time from M to W, we get the time
from E to W plus the time from M to R. The
times from E to R and M to W each include one
3-minute stop, whilst the time from E to W
includes two 3-minute stops, so when we
subtract the EW time from the sum of the ER
and MW times, the stops cancel out. Thus the
time from M to R is 24 + 36 − 42 = 18 minutes.
We can now look further at an extra useful
element in the solution of problem-solving
There is one railway on the island of Mornia,
which runs from Enderby to Widmouth. There
are two intermediate stops at Maintown and
Riverford. The trains run continuously from
one end to the other at a constant speed,
stopping for three minutes at each station.
From departing Enderby to arriving at
Widmouth takes 42 minutes. From Enderby to
Riverford takes 24 minutes. From Maintown
to Widmouth takes 36 minutes.
How long does it take from Maintown to
Riverford?
Activity