Thinking Skills: Critical Thinking and Problem Solving

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