[問題]PREP-T1-Q153 (PS)

[scottkidd]

153. 15903-!-item-!-187;#058&010559
A boat traveled upstream a distance of 90 miles at an average speed of (v - 3) miles per hour and then traveled the same distance downstream at an average speed of (v + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

(A) 2.5
(B) 2.4
(C) 2.3
(D) 2.2
(E) 2.1

Ans:A

這題我的解法是：
90/(v-3)-90/(v+3)=0.5
算出v再去代回90/(v+3)去求時間，不過這樣的解法會變成要解一元二次方程式，
得花不少時間計算，請問這題有xdjm有比較快的算法嗎？

[little8]

頂一下
因為我也不知道這題怎麼算哩
感謝大大出面相救~~

[chris8888]

這題出現一元二次方程式但卻非常簡單, ETS常常出考題會讓你以為算不下去, 事實上, 都可以化簡, 所以不可以跳步不算, 萬不可單單用看的

90/(v-3) - 1/2 = 90/(v+3)
全部乘上 (v+3)(v-3)
90(v+3) - 1/2(v+3)(v-3) = 90(v-3)
90v + 270 = 90v - 270 + 1/2(v^2 - 3^2) <== 把90v化簡
540 = 1/2(v^2 - 3^2)
1080 = v^2 - 9
1089 = v^2

因式分解, 抓因數 1089 = 3^2 * 11^2 ; 得33

so travel downstream took the ship 90/33+3 to finish the trip, finally we can get 2.5 hours