You pay tax in both states. The income you earn in each state is taxed by that state. It doesn't matter whether it's on the same day or different days. The payment of tax is determined by where you earned the income, not day by day. If you work in two states in one day, you pay tax to both states, on the income that you earned in each state.

All your income is taxed by the state that you live in, no matter where you earn it. In most cases your tax return for the state that you live in will give you a credit for tax that you pay to other states. To be able to give you more specific information, we would need to know the particular states involved, and which state you live in.

The general  rule is you pay tax to the non resident state on the income you earn there. You also pay tax on ALL your income to the resident state, but get a credit (or partial credit) for the tax you paid to the non resident state.

But it depends on the circumstances and the states. Man neighboring states  have "reciprocal agreements" on wages, and it is not necessary to pay tax to the non resident state.  

Also see this about  business Trips. http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/  If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.