Stack Overflow provides a platform for developers to seek suitable solutions by asking questions and receiving answers on various topics. However, many questions are usually not answered quickly enough. Since the questioners are eager to know the specific time interval at which a question can be answered, it becomes an important task for Stack Overflow to feedback the answer time to the question. To address this issue, we propose a model for predicting the answer time of questions, named Predicting Answer Time (i.e., PAT model), which consists of two parts: a feature acquisition and fusion model, and a deep neural network model. The framework uses a variety of features mined from questions in Stack Overflow, including the question description, question title, question tags, the creation time of the question, and other temporal features. These features are fused and fed into the deep neural network to predict the answer time of the question. As a case study, post data from Stack Overflow are used to assess the model. We use traditional regression algorithms as the baselines, such as Linear Regression, K-Nearest Neighbors Regression, Support Vector Regression, Multilayer Perceptron Regression, and Random Forest Regression. Experimental results show that the PAT model can predict the answer time of questions more accurately than traditional regression algorithms, and shorten the error of the predicted answer time by nearly 10 hours.