Question

牛吃草问题公式

Answer 1

1）草的生长速度＝（对应的牛头数×吃的较多天数－相应的牛头数×吃的较少天数）÷（吃的较多天数－吃的较少天数）；
2）原有草量＝牛头数×吃的天数－草的生长速度×吃的天数；`
牛吃草3）吃的天数＝原有草量÷（牛头数－草的生长速度）；
4）牛头数＝原有草量÷吃的天数＋草的生长速度。

追问

举个例子

追答

例如：有一块牧场，可供10头牛吃20天，15头牛吃10天，则它可供25头牛吃多少天？
解：(200-150)/(20-10)=5（草的生长速度）
10*20-5*20=100 （原有草量）
100/(25-5)=5(天）

追问

如果是求牛的头数呢？题目。

追答

例如：有一块牧场，可供10头牛吃20天，15头牛吃10天，则它可供多少头牛吃5天？
解：(20*10-10*15)/(20-10)=5（草的生长速度）
10*20-5*20=100 （原有草量）
牛头数＝原有草量÷吃的天数＋草的生长速度=100÷5＋5=20+5=25（头）

Answer 2

数字法:
1）草的生长速度＝（对应的牛头数×吃的较多天数－相应的牛头数×吃的较少天数）÷（吃的较多天数－吃的较少天数）；
2）原有草量＝牛头数×吃的天数－草的生长速度×吃的天数；` 3）吃的天数＝原有草量÷（牛头数－草的生长速度）；
4）牛头数＝原有草量÷吃的天数＋草的生长速度。
方程法:A头牛能够B天将草吃完,C头牛能够D天将草吃完,N头牛能够W天将草吃完? (N或W只有一个未知,按情况而定,而ABCD都是已知)
假设一头牛一天的吃草量为M，N头牛能够W天将草吃完；原有草量为Y，草每天的生长量为X，得到如下方程组：
Y=(A－X)B Y=(C－X)D Y=(N－X)W 或

ABM=Y+BX CDM=Y+DX NWM=Y+WX
解得(N= 或W= ) Y= X=

Answer 3

有一片牧场上长满牧草，每天草以匀速生长。这个牧场可供17牛吃30天或19牛吃24天。现有若干头牛吃草，6天后，4头牛死亡，余下的牛吃了2天将草吃完，求原有牛的头数。

Answer 4

Answer 5

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