A tree casts a 30-foot shadow at the same time a 6-foot tall man casts a 4-foot shadow. What is the height of the tree?

Because they are at the same time, the ratio of the length of the shadow of the man to the height of the man is the same as the ratio of the length of the shadow of the tree to the height of the tree.

The length of shadow of the man is 2/3 the height of the man. 

(4/6 is the same as 2/3.) 

So, the length of the shadow of the tree (30 feet) is 2/3 the height of the tree. 

30 = (2/3) * T , where T is height of the tree. Solve for T

A tree casts a 30-foot shadow at the same time 

a 6-foot tall man casts a 4-foot shadow. 

30/x = 4/6, x = 180/4 = 45

The height of the tree is 45 feet.