2015年4月19日 星期日
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!
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