Half of robert's piece of wire is equal to 2 thirds of maria's wire. the total lenght of their wire is 10 feet. how much longer is robert's wire than maria's?

You have a system of equations here. R=Robert's piece of wire M=Maria's piece of wire

R/2=2M/3
and
R+M=10

With some basic algebra, you can make that first equation into
R=4M/3
then use substitution to get
(4M/3)+M=10
Then solve for M
(4M/3)+(3M/3)=10
7M/3=10
7M=30
M=30/7

so Maria's wire is 30/7 feet long. With a little more substitution, we can get:
R+(30/7)=10
R=10-(30/7)
R=(70/7)-(30/7)
R=40/7 feet long

So your final answer would be that Robert's wire is 10/7 feet longer than Maria's (which you could always put into decimal form)

They are somewhat similar