If a man casts 14 foot and a child casts a 9'4" shadow at the same time how tall is the man?
How tall is the child?
2 feet
To determine the height of the man, we can use a proportion based on the length of the shadow cast by the man and the length of his actual height. Here's how you can solve it step by step:
1. Convert the length of the child's shadow from feet and inches to just inches. Since there are 12 inches in one foot, we can calculate:
9 feet x 12 inches/foot = 108 inches
108 inches + 4 inches = 112 inches
So, the child's shadow is equivalent to 112 inches.
2. Set up a proportion to find the height of the man. Let's represent the height of the man as "x":
child's shadow (112 inches) / man's height (x) = man's shadow (14 feet)
3. Since the child's shadow (112 inches) is equivalent to the man's shadow (14 feet), we can write the proportion as:
112 inches / x = 14 feet
4. Convert the length of the man's shadow from feet to inches:
14 feet x 12 inches/foot = 168 inches
5. Now we can rewrite the proportion as:
112 inches / x = 168 inches
6. Cross-multiply the equation:
112 inches * x = 168 inches
7. Solve for "x" by dividing both sides of the equation by 112 inches:
x = 168 inches / 112 inches
8. Simplify the division:
x = 1.5
Therefore, the height of the man is 1.5 times the length of the child's height, which means the man is 1.5 times taller than the child.