Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
420
© 2014 Pacific Crest
Scenario:
Suppose you have a clock that stopped working. You know the initial time that it
stopped at and how much time has elapsed since. Construct a mathematical model
to calculate the correct final time. Example: A clock stopped at 5:57pm 23 hours
and 45 minutes ago
Step
Watch it Work!
1.
What is your
purpose?
How do you update a clock given the stopped clock time and the elapsed
time?
2.
Gain background
knowledge
Recall knowledge of hours, minutes, and clock time.
3.
What is important?
The model will include the hours and minutes for the initial, final, and
elapsed times in military time
4.
What can be
ignored?
We will ignore any fractional part of a minute.
5.
Establish
relationships
Final time is the sum of initial time and elapsed time. Clock numbers use
modular arithmetic and cycle from 59 back to 0 for minutes (mod(60)) and
23 back to 0 (mod(24)) for hours.
6.
Abstract a model
from the problem
Initial Time H
i
: M
i
Elapsed Time H
e
: M
e
Final Time H
f
: M
f
M
f
=(M
i
+ M
e
)mod(60)
H
f
=(H
i
+ H
e
+ H
x
)mod(24)
H
x
=1 if M
i
+ M
e
≥ 60, 0 otherwise
7.
Reframe the
problem
Converting 12 hour times to military time we get the values
H
i
= 17 M
i
= 57 H
e
= 23 M
e
= 45
8.
Find a solution
M
f
=(102)mod(60) = 42
H
f
=(41)mod(24) = 17
9.
Test the model
The model gives a time of 17:42. The current time is 17:43.
10.
Improve the model
We return to step 3 and include the number of seconds in our model to
provide a more accurate final time.
YOUR
TURN!
Scenario:
Suppose you can complete an assignment in 3 hours and another student can
complete it in 4 hours. How long would it take if you worked together?
O
ops
! A
voiding
C
ommon
E
rrors
●
Inadequate background knowledge
Example
: Reinventing the wheel
Why?
Outside your discipline, you failed to notice that varieties of suitable models have
already been developed and published in the literature.