求解math两道

billchen_hikaru

A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row.  The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her.  How many such arrangements of the 6 people are possible?

A.      5

B.      6

C.      9

D.     24

E.      36

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y.  At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A.      4

B.      6

C.      8

D.     10

E.      12

primefangs

第一题偶先想到最矮的一定在前排,最高的一定在后排,

然后就穷举, 比如从矮到高算是1 2 3 4 5 6, 那么就看2 3 4 5 的排列了,

举出来, 能站后排的有五种情况: 246,256,346,356,456

第二题, 总体感觉老老实实算的话,计算的量还是有点大的, 如下:

设machine X 的每日productive is x, machine Y 的每日productive is y.

所以根据第一个条件能列出: w/x-2=w/y 推出 : y=xw/w-2x

然后根据第二个条件能列出: 3(x+y)=5w/4

把y=xw/w-2x代入3(x+y)=5w/4中可得: 24x^2-34wx+5w^2=0, 得出: x=5w/4 (根据题意可知x要完成w的量必定大于2天,所以排除) 或 x=w/6

得出答案d=2w/w/6z ]\

primefangs

得出答案:d=2w/w*6