Personalized news recommendation can help users stay on top of the current affairs without being overwhelmed by the endless torrents of online news. However, the freshness or timeliness of news has been largely ignored by current news recommendation systems. In this paper, we propose a novel approach dubbed HyperNews which explicitly models the effect of timeliness on news recommendation. Furthermore, we introduce an auxiliary task of predicting the so-called "active-time" that users spend on each news article. Our key finding is that it is beneficial to address the problem of news recommendation together with the related problem of active-time prediction in a multi-task learning framework. Specifically, we train a double-task deep neural network (with a built-in timeliness module) to carry out news recommendation and active-time prediction simultaneously. To the best of our knowledge, such a "kill-two-birds-with-one-stone" solution has seldom been tried in the field of news recommendation before. Our extensive experiments on real-life news datasets have not only confirmed the mutual reinforcement of news recommendation and active-time prediction but also demonstrated significant performance improvements over state-of-the-art news recommendation techniques.