Simultaneous equations
長い文章問題です。お時間ある方がおられれば宜しくお願い致します。
~ 問題 PART A ~
Pamela has started training to build herself up for the Summer triathlon competitions.
She goes on short training runs with a mixture of running, bike riding and swimming. Pamela keeps accurate times for each of the disciplines.
On day one she ran for 24 minutes, biked for 9 minutes and swam for 10 minutes for a total distance of 10 680 meters.
On day two she ran for 18 minutes, biked for 15 minutes and swam for 12 minutes covering a distance of 12 750 meters.
On day three Pamela ran for 12 minutes, biked for 20 minutes and swam for 14 minutes for a total of 14 270 meters.
Calculate the speed she swims at in meters per minute.
これは問題なく R = 220, B = 550, S = 45 と解けます。答えも合っていました。
~ 問題 PART B ~
Pamela’s coach asked her about the Day one figures.
He said that if she spent one minute more time biking ( a total of 10 minutes biking) her total distance on day would be different. Calculate the new total distance for her based on our calculations in Part A。
On day one she run for 24 minutes, biked for 10 minutes and swam for 10 minutes. What is her total distance?
Her coach said that if they had used this distance for Day one then working out her swimming speed would have been difficult.
Investigate her swimming speed using:
On day one she ran for 24 minutes, biked for 10 minutes and swam for 10 minutes for a total distance you have calculated.
On day two she ran for 18 minutes, biked for 15 minutes and swam for 12 minutes covering a distance of 12 750 meters.
On day three Pamela ran for 12 minutes, biked for 20 minutes and swam for 14 minutes for a total of 14 270 meters.
Why does this combination of times cause a problem when your solution from Part A still gives a correct solution? Prove that your explanation is correct by finding another correct solution to your new system of equations.
式を立てて解いていくと最後は 0 = 0 となってしまいます。こうなると解は無数に存在する、という事になりますよね？ これから先どうやったらいいのかわかりません。
答えは
[In addition to correctly showing there is no unique solution the student correctly shows that
R = 220, B = 550, S = 45 is still a solution.
The student explains why there is now a unique solution. The student finds at least one other solution such as
R = 217.5 , B = 541 and S = 60
As predicted by
S = k, B = 577 - 0.6k and R = 227.5 - 0.16667k ] となっていますがこの説明がわかりません。
質問
(1) R = 217.5 , B = 541 and S = 60 ← この数字はどこから出てくるのですか？
かならずしもこの数字でなくともいいのでしょうが、これは回答者が適当に出した数字ですか？
(2) S = k, B = 577 - 0.6k and R = 227.5 - 0.16667k ← この数字もどこから出てくるのかわかりません。又、kは何を表すのかもわかりません。
読んだ下さり有り難うございました。
