Algebra word problem

Question

You want to find the height of a tall tree. On a sunny day you measure the length of the shadow of the tree and find that it is 12 feet 5 inches long. At the same time you measure the shadow cast by a 5-foot fence post and find that it is 3 feet 4 inches long. How tall is the tree?

Answer 1

1. Convert to common units (inches):

Fence height = 5 feet = 5 feet * 12 inches / foot

= 60 inches

Fence shadow = 3 feet. 4 inches

3 feet * 12 inches / foot = 36 inches

36 inches + 4 inches = 40 inches

Tree shadow = 12 feet, 5 inches

12 feet * 12 inches / foot = 144 inches

144 inches + 5 inches = 149 inches

2. Set up the proportion equation:

Tree height / Tree shadow length =

Fence height / Fence shadow length

Substitute the actual numerical values for the corresponding items above:

x / 149 inches = 60 inches / 40 inches = 6/4 = 3/2

Multiply both sides by 149 inches:

x = (3/2) * 149 inches

x = 223.5 inches

Convert to feet:

223.5 inches / ( 12 inches / foot)

= 18.625 feet

Convert the decimal fraction of a foot to inches:

0.625 foot * 12 inches per foot = 7.5 inches

You can check on a calculator that 223.5/149 =3/2

Tree height = 18 feet, 7.5 inches

Answer 2

t/12'5 = 5/3'4

12 feet 5 inches = 149 inches

3 feet 4 inches = 40 inches

t/149 = 5/40= 1/8

t = 149/8 = 18 5/8 feet

t = 18 feet 7 1/2 inches = the tree's height