1. Figuring out distance, etc...??

If a 5 cm piece of wire is cut into two parts such that a square is formed by bending one part will have four times the area of a square formed by bending the other part, what is the length of the longer part?

A jet pilot plans to cover a 1000-km course at an average speed of 1000 km/h. For the first 800 km the speed is 800 km/h. At what rate must the remaining distance be covered?

2. Originally Posted by EyesThatSparkle02
If a 5 cm piece of wire is cut into two parts such that a square is formed by bending one part will have four times the area of a square formed by bending the other part, what is the length of the longer part?
You need to assign variables to some things in this problem. Since you are dealing with lengths and areas (which are determine by the lengths) and because ultimately you need to know a length, it seems that the lengths of the wires are important. Lets make each length a variable - say x and y. If the total length is 5, can you come up with an equation relating x to y?

Also, what would be the length of a side of a square made out of the wire that's x cm long? What would be its area (in terms of x)? What would be the area of the square made from the y cm length? Can you come up with an equation relating these areas?

Once you have two equations dealing with these two variables, you should be able to solve them by one of the methods used to solve systems of equations. Substitution for example (solve both for y and the you know that these will equal each other since they both equal y).