I think the short answer is probably yes. Under both Federal and state law, travel time should be paid if you perform any work that is deemed to be an “integral and indispensable” part of your main work activities. These activities include picking up and transporting necessary equipment or receiving work instructions at a meeting point prior to traveling to the work site.
You should contact an experienced employment attorney as it can be a rather fact intensive question.
Based on the facts in your question it seems very likely that your work day starts and ends when you get to / drop off the work vehicle. So the time it takes for you to drive the work vehicle to / from the job site should be included in your paid hours.
You should confirm this with an attorney in your area that specializes in employment law.
Yes, you are entitled to the drive time. This issue is complicated if you are allowed to take the company truck home with you such that it might be considered a commute, but the facts you relate clearly call for being paid from door to door when you leave the place of business and return to the place of business.
Your issue will be how to proceed, and when, to enforce your rights. You have several options, starting with complaining directly to the employer, and then if that does not work, you can make legal claim in small claims court or superior court, or an administrative claim in the Labor Commissioner's Office, also known as the Division of Labor Standards Enforcement.
The other issue is timing. You may be financially dependent on your present job. If so, it might be foolish to immediately place your job in jeopardy by making a claim against your employer upon who you are dependent. The unfortunate truth is that although retaliation for making such claim is unlawful, it happens, and in ways that are often impossible to prove as retaliation. Your best approach might be to keep very good records of the time you spend for which you are not receiving compensation until you find new employment and then make a claim once you are no longer financially dependent on this employer. You have at least three years from each date you should have been paid to make a claim, and four years if you go the superior court route.
You should locate and consult with an experienced employment law attorney about this. You can find one on this site in the Find a Lawyer section, or you can find many good experienced employment law attorneys at www.cela.org, the home page of the California Employment Lawyers Association, an organization whose members are dedicated to the protection of employee rights. You can find a database of its members on that site, categorized by city and practice areas.
Good luck to you.
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I agree with the previous answers. From the facts presented in your question, it appears you SHOULD be paid for the time you drive to and from the job site. You should contact an attorney with experience in California wage and hour laws regarding your case.