Cara likes candles. she also likes mathematics and was thinking about using algebra to answer a question that she had about two of her candles. her taller candle is 12 centimeters tall. each hour it burns makes the candle lose 2.25 centimeters in height. her short candle is 10 centimeters tall and loses 1 centimeters in height for each hour that it burns.

cara started filling out a table to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. create the table for cara. use the data in the table to determine what time the two candles will be at the same height.

also, she wants to know what height the two candles would be at that time. if it is not possible, she wants to know why it could not happen and what would need to be true in order for them to be able to reach the same height. to cara understand what you are doing, justify your results. you will explain your thinking using a created table and created graphical representation of the situation.

1. create the table, and use it to write an equation for the height of each candle in terms of the number of hours it has burned. be sure to include any constraints for the equation.

create a graphical representation of your data, taking into account natural restrictions on domain, range, etc.

cara has another candle that is 14 cm tall. how fast must it burn in order to be 8 cm tall after 4 hours? explain your thinking.