Thinking Skills: Critical Thinking and Problem Solving

218 Unit 5 Advanced problem solving

start one 360º revolution nish

It is quicker to lower a tall stone than to

raise it. From experience, a stonemason

knows that he can turn a stone through 90°

in ()bh minutes, where b is the length of the

face that is flat on the ground, and h is the

vertical height of the stone as he is about to

turn it.

For example, a block that has two of

its dimensions as 5 metres and 2 metres

can be turned 180° in ()^52 minutes + ()^25

minutes = 2 minutes 54 seconds.

The stonemason wishes to move large

blocks of stone, in order to then cut them

into manageable pieces for tombstones.

He is considering how to move them most

quickly.

In order to move a block, he chooses the

initial orientation, and then rolls it in the

same direction for the whole journey.

(A calculator or computer spreadsheet will be

useful for these assignments.)

1    Duane and Mervin are going to town, a

distance of 12 km. They have only one bike

between them, so they decide that one

should ride a certain distance while the

other walks. The cyclist will then leave the

bike by the side of the track for the walker

to pick up when he arrives, and continue

on foot. The walker will then ride the same

distance; and they will repeat the process

until they get to town. Duane rides at

15 km/h and walks at 6 km/h. Mervin

rides at 20 km/h and walks at 4 km/h.

How long does it take until they both

reach town if they use the best strategy?

If you have time, you may consider

what would happen if they cycle different

distances: can the time for them both to

arrive in town be improved?

2    Study the information below and answer

the questions. Show your working.

Large blocks of stone can be moved by

‘rolling’ them. The diagram below shows

how a single stone can be moved in

this way.

End-of-chapter assignments

•   We have seen how models can be

developed for a variety of situations that

allow the prediction of what will happen if

certain variables change.

•   A model can be used to carry out ‘what if?’

analyses.

•   When answering more complex questions,

it is important to remember what is

required and to reread the material and

question if necessary to check that all

the important information has been

incorporated.

•   In order to get better marks in higher-level

examinations, it may be necessary to do

extra work and to think carefully to improve

the quality of the answer.

Summary