In the United States, I think the best answer here is it depends. As @DA mentioned in the comments, there is no federal law regarding this particular aspect of voting rights. The states (some of them anyway) have stepped up, and I found a pretty useful link here that summarizes the current patchwork of laws. (It looks like DA found that same link. Great minds I guess.)
NB: It looks like that page was made for the 2012 election, so I am taking those summaries to be accurate as of that timeframe.
I think the best summary of the current status of whether or not your boss is required to allow you to "take off" to go vote comes from here:
I'm scheduled to work on Election Day. Do I have a right to take time off from work to vote?
Not necessarily. Depending on where you live, the answer may be "yes, definitely," "no, not really," or "it depends." This is an area of the law dealt with on a state-by-state basis, even during the national presidential elections held every four years. So your right to vote during work time depends on what your state law says.
Looking through the list from the first link, it looks like there's a few broad categories of the types of laws states have (or failed to have) enacted:
1. No specific law requiring time off to vote. (21 total)
Connecticut, D.C., Delaware, Florida, Idaho, Indiana, Louisiana, Maine, Michigan, Mississippi, Montana, New Hampshire, New Jersey, North Carolina, North Dakota*, Oregon, Pennsylvania, Rhode Island, South Carolina, Vermont, Virginia
I am including North Dakota in this list, even though the law "encourages employers to [allow time off of work to vote]" because encourging something is wholly distinct from requiring it.
2. Employees who begin their work day less than X hours after polls open and finish less than X hours before polls close are entitled to Y hours leave to vote (25 total)
Alabama, Alaska, Arizona, California, Colorado, Georgia, Hawaii, Illinois, Iowa, Kansas, Maryland, Missouri, Nebraska, Nevada, New Mexico, New York, Oklahoma, South Dakota, Tennessee, Texas, Utah, Washington, West Virginia, Wisconsin, Wyoming
It should be noted here that each of these states' laws are worded somewhat differently with somewhat different restrictions. For instance, in Tennessee the employee must request leave by noon the day before Election Day.
3. Employees may take X hours off to go vote (2 Total)
Kentucky, Minnesota
In Minnesota, those hours are specified to be in the 'morning'.
This being the United States, there are some notable outliers.
Arkansas
Employers must create schedules so that each employee will have the opportunity to vote.
That's seems fair enough to me.
Massachusetts
No employee of a manufacturing, mechanical or mercantile establishment must work during the first two hours after the polls open if the employee applied for a leave of absence during this period.
Apparently the rest of us are out of luck if our employers don't want us to vote.
Ohio
Employers cannot fire or threaten to fire an employee for taking a reasonable amount of time to vote. Paid only for salaried employees.
And (my personal favorite)...
Puerto Rico
Election day is a legal holiday in Puerto Rico and most employees have the day off work. Employers running a business in operation on election day, however, must establish shifts allowing employees to go to the polls between 8am and 3pm.
In Regards To Travel
It is my impression that none of the states have laws on the books that take this into account. So while you may be entitled to have the morning off to go to the polls, you may be physically unable to reach your polling station depending on where your employer had you travel to on the day prior to election day. You still have a right to vote, but I would consult your local board of elections and acquire an absentee ballot in order to have your voice heard.