There is no

*5x* in the solution.

We denote the whole distance by

*x*. Therefore each part of the distance is less than

*x* (some fraction of it).

"Tim traveled 40 percent of the distance of his trip alone,"

0.4

*x*"continued another 20 miles with Sam"

20 miles

"and then finished the last half of the trip alone."

0.5

*x*The resulting equation is:

0.4

*x* + 20 + 0.5

*x* =

*x*.