中一數學之方程應用題(續)

上回說過：「每條文字題總有一句終極說話，能真正助你列式的。」

這次我要自摑一下嘴巴了！先看看題目。

Stephanie is a cyclist. By what percentage must she increase her average speed in order to reduce by 10% the time a particular journey takes?

怎麼樣？怎也找不到那句「終極說話」罷？原來世上有些事情是不說自明的，即所謂common sense。處理這條題目須用上 conservation的 concept。嘩，乜鬼嚟嫁？唔好吓吓講埋 D雞腸專有名詞來唬人！唔係嚇你，講事實啫，conservation其實不是什麼高深概念，說穿了只是「不變」的意思。

你把水從一個小圓杯倒進一個大方杯裡去，水的形狀變了，水位低了，然而什麼是不變的？是水的體積，即 conservation of volume。話說回來，這條題目中有什麼是不變的？是 distance of the journey罷，你走的是同一條路，是十公里便是十公里，不因快慢而不同。這個可否說是 common sense？正如母親是女人，需要說出來嗎？

既然如此，即那暗藏的「終極說話」是：
 distance travelled with the original speed = distance travelled with the new speed

let s be the original speed and t be the time taken in the original journey, then the new speed should be s(1+y%) and the new time taken should be t(1-10%).

 distance travelled with the original speed = distance travelled with the new speed
          original speed x original time taken = new speed x new time taken
                                                   st = s(1+y%)t(1-10%)
                                                    1 = (1+y%)(1-10%)
                                              1/0.9 = 1+y%
　　　　　　　　　　　　　1+1/9 = 1+y%
　　　　　　　　　　　　　　　y = 11.1% (3 sig. figs.)
Therefore she has to increase her speed by 11.1%.

數學不只考計數，還考 common sense！