San Diego State University Different Approaches to Problems

Please do 5, 9, 11 and 13.

15.3 Different Approaches to Problems
Different Approaches to Problems
Approach 1: Table
Make a table that shows Aña’s and Bea’s positions every minute. If the positions are ever equal
before the race is over, then Aña has caught up. Here are two versions of such a table:
Time
(min)
Aña’s
position (m)
Bea’s
position (m)
0
0
600
1
225
800
2
450
1000
3
675
1200
4
900
1400
5
1125
1600
⋮
⋮
⋮
Time
(min)
Aña’s
position
(m)
Bea’s
position (m)
0
0
600
5
1125
1200
10
2250
2600
15
3375
3600
20
4500
4600
25
5625
5600
Version 1, with positions recorded at each minute, might even make you think that Aña would never catch up! But if we add
a fourth column that records Aña’s distance behind Bea, we would see that Aña is catching up, but only by 25 m/min.
Version 2 recognizes that Aña is going to take several minutes to catch up and records positions every 5 min. Again, adding a
fourth column showing how far Aña is behind Bea might be helpful. The Version 2 table does show that Aña is ahead after 25
min, so she has caught up. A little more calculation (or a lot more for the Version 1 table) shows that Aña catches up after 24
min, when both have run 5400 m.
Different Approaches to Problems
Different Approaches to Problems
Different Approaches to Problems
15.4 Average Speed and Weighted Averages
Average Speed and Weighted Averages
Average Speed and Weighted Averages
Average Speed and Weighted Averages
Average Speed and Weighted Averages