I live in Chattanooga TN. I need to know how much per hour to charge for mowing and cleaning a house?

No less than minimum wage. It’s against the law for them to pay you any less. Call some businesses in the area and ask what they charge.

Mowing a lawn is based on its size and what is expected of the owner. generally, an average-size lawn is about $45.00 for both front and back with some weedeating. additional work is really based on the individual grasscutter and the owners agreed decision.

Housecleaning is also based on the above.

I live in Memphis. I would pay $15—$25 an hour for someone to clean my house if I was supplying the cleaning supplies. For my lawn I think I paid $100 per cut a few years back. My lawn is about an acre and a half. Takes about 2 hours to cut and edge.

Call some people who do the service like you are interested in hiring them, and ask how much they charge, so you know what the competition is.

I would have thought between $12 and 15 dollars an hour.

You might find this link helpful, as it lists everything you need to know about starting a cleaning service, including links to the IRS pages about being self-employed and paying taxes on your income from a cleaning service. The income is taxable.

Envision the project. If you leave your house at 8am, ½ hour travel time, 2 hours to cut the grass,½ hour travel time back, you have 3 hours invested. If you charge $15 an hour, you will have $30 in your pocket. Ask yourself if you would be happy at 11am when you get back home with 30 dollars in your pocket. If you charge $50 you would have $100 for three hours of your time. Every customer would prefer $100 but if $30 is enough for you, charge $15/hour.
Having said that, set a “mental minimum” so that you feel valued enough during the work that you will do a good job. If you take the job for less than you feel it is worth, it is very difficult to do a quality job. When you perform a job for someone else for money, you sign your name to everything you do for them.
Call 2 lawn care services in the area to get price quotes. If your mental minimum is 15/hour and everyone else charges 75/hour, you could charge 45/hour. The customer gets a great deal and you make good money. Do the same market research with the house cleaning job.
The two other considerations are “parts” and weather this is a one time job or repeating. A repeating job can warrant a discount sometimes. “Parts” include everything you would spend to do the job ie gas, oil, weedeater line, water to drink, snacks, cleaning supplies, buckets, rags, etc. Good Luck, I hope you get the job.