Thinking Skills: Critical Thinking and Problem Solving

90 Unit 3 Problem solving: basic skills

3.4 Processing data

In the previous chapter we looked at solving

problems by selecting the correct items of data

from various sources and using them in the

correct way to produce a solution. This chapter

considers problems where the required data is

clearly given (i.e. there is no ambiguity about

which pieces of data to use). The problems

covered here involve using the data in the

correct way to find the solution to the

problem. The activity below illustrates this.

Luiz and Bianca are brother and sister and go

to the same school. Luiz walks to school

using a footpath, a distance of 900 m, and

he walks at 1.5 m/s. Bianca cycles to school

along the roads, a distance of 1.5 km, and

she cycles at 5 m/s. They both plan on

arriving at school by 8.55 a.m. Who leaves

home first and by how much?

A Bianca, by 5 minutes

B Luiz, by 5 minutes

C They leave at the same time

D Bianca, by 10 minutes

E Luiz, by 10 minutes

Activity

Commentary

The skill in this question is to use the correct

pieces of information appropriately and at the

right time in the calculation. There are five

relevant pieces of data (the two distances, the

two speeds and the fact that they arrive at the

same time). It is quite clear that the method

of solution is to calculate each of the journey

times, so in this case there is no method to

find. Problems where the method is not clear

will be discussed in the next chapter.

Luiz walks 900 m at 1.5 m/s, so this takes

him 900 ÷ 1.5 = 600 seconds or 10 minutes.

Bianca cycles 1.5 km (1500 m) at 5 m/s, which

takes her 1500 ÷ 5 = 300 seconds or 5 minutes.

As Luiz takes 5 minutes more, he must leave

home 5 minutes earlier, so B is correct. (If you

are unsure about relating speed, distance and

time, see the advice below.)

This is a multiple-choice question, a type

you will see frequently in thinking skills

examinations. Some of the activities in this

section of the book have multiple-choice

answers, as in the examinations. However,

many have ‘open’ answers, where you are

asked, for example, to give a numerical

solution. This is, in many ways, a better way to

learn how to do the questions – you will be

able to select the correct multiple-choice

answers more easily if you can do the question

without needing to know possible answers. If

you can come to the solution without looking

at the options and then check that your

solution is one of the options, this is safer and

often quicker than checking the options

against the data given. In the case of the

example above, it is much better to work out

the answer first.

Speeds, distances and times

Many problem-solving questions involve

calculating one of the variables speed,

distance or time from the other two. If you

are uncertain how to do this, the formulae

below give the method:

speed = distance/time

distance = speed × time

time = distance/speed