r for Robert's piece, m for Maria's.
[tex] \frac 1 2 r = \frac 2 3 m[/tex]
[tex]r = \frac 4 3 m[/tex]
[tex]r + m = 10[/tex]
[tex] \frac 4 3 m + m = 10[/tex]
[tex]\frac 7 3 m = 10[/tex]
[tex]m = \frac{30}{7}[/tex]
[tex]r = \frac 4 3 m = \frac{40}{7}[/tex]
[tex]r - m = \frac{40}{7}- \frac{30}{7} = \frac{10}{7}[/tex]
Answer: 10/7 feet
Check: 1/2(40/7) = 20/7, 2/3(30/7) = 20/7. they match, good.
40/7 + 30/7 = 70/7 = 10, good
