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)