Andrea notices that the 40-foot tree next to her is casting a 10-foot shadow. How tall, in inches, is Andrea if she is casting a 18-inch shadow at the same time?
Andrea is 68 inches tall.
I'm not entirely confident this answer is correct, as I got a different answer when I did my calculations. Also, it's not terribly helpful to recieve an answer without an explanation to go with it.
If the person doesn't know how to solve the problem, then they don't learn how to solve it in the future. The objective of most teachers is self-obsoletion (in effect, they are tryhing to do their job, so they aren't necessary, in order to succeed.) This forum could also be viewed the same way, as we would like to answer the questions in a way that lets the people solve the remaining ones on their own.
I started by observing the height-of-object to length-of-shadow ratio. We're given both values for the tree, so we simply divide: 40 foot height/10 foot shadow = 4:1 ratio of height:shadow size.
Andrea's shadow is 18 inches long, so we place it into the ratio. 18 inches (Andrea's shadow)/1 (ratio component relating to shadow size) = 18 inches, so we multiply the first value by 18 inches.
This yields 72 inches, rather than 68, as the guest below suggested.
On an exit note, being a little bit taller than normal, I would be somewhat intimidated by someone who's a full 6 feet tall.