數學Rational expressions

Question

請幫我解答這3題數學題
1. A plane takes the same amount of time to fly 1500 km at 100km/h below its top speed as it takes to fly 1250 km at 200/h below its top speed. What is the plant's top speed, in kilmetres per hour?

2. The average speed of a plane is eight times as great as the averge speed of a train. The plane takes 8 3/4 hours less than the train to travel 1050 km. Find the average speed of the plane and the average speed of the train?

3. Dividing 108 by one more than a number gives the same result as dividing 72 by three less than the number. What is the number?

請問你怎麼知道要用什麼來除的 還有算式怎麼百
在台灣這個數學是哪一年級教的?

Answer 1

3.
一個數 x 加 1, 去除 108, 和 x 減 3 去除 72 結果一樣,
所以 108/(x+1) = 72/(x-3), 或 72(x+1) = 108 (x-3),
或 (108-72)x = 72 + 324, 或 36x = 396, 或 x = 11


2. Let P be the plane speed and T be the train speed.
P = 8T and 1050/P = 1050/T - 8 3/4
So, 1050/(8T) = 1050/T - 35/4
So, T = 1050x7x4/35/8 = 105 km/hr
and P = 840 km/hr

1. Let the top speed be T.
1500 / (T - 100) = 1250 / (T - 200)
1250 (T-100) = 1500 (T-200)
250 T = 300000 -125000 = 175000
T = 700 km/h

2007-07-18 10:01:18 補充：
> 用什麼來除的?
第一題是由題意得知. 第二, 三是因為時間為距離除以速度

> 哪一年級教的?
我不確定. 我的小孩當初是:
設未知數為變數來解, 解的時候用到代數運算, 是國中的內容.
但小學也有教這觀念, 只是沒有明白的設變數,
通常是把未知數用一個小方塊代表.
當然, 這些題目較簡單, 不用變數也可解的.