Our hope is our vision of the possible. We need not hope that the sun will shine. We have hope in those things that are possible, but not yet attained. It is this future perspective that defines hope. There is no hope that the past will change, but only the future.
Mankind may have hope in all kinds of future events, but the one that is related to faith is the hope of the promised blessings of the eternities. God has made the promise. This same God who fulfilled his promise to send the Atoning Messiah has promised that if we obey the commandments and endure to the end, then we may enjoy the blessings of heaven. We do not enjoy them on earth. We cannot fully enjoy them on earth. However, we can look forward to those blessings, and know that they are possible. This is where hope and faith become intertwined.
Faith is a mechanism of action. Hope is not. Hope cannot replace faith, for it is entirely possible to hope without any action that might accomplish the hope. We might hope to become very wealthy, but decline to work toward that end. On the other hand, faith carries within its definition the need to act. Therefore the two principles work together. We have hope for something in which we can have the faith to believe, act, and attempt to achieve.