I live in a 1 1/2 story home built in the 50's the roof pitch is steep. A family room was added a few years ago and the roof slope is moderate. The problem occurs in the winter with snow. The rear of the house faces west and the warm sun in the spring or a warm winter day melts the snow off of the original roof. This melt water runs off then runs onto the roof of the family room which is attached to the original but with a gentler slope. Water backs up under the shingles, because the snow on the addition has not melted, and leaks into the family room. This is an ongoing problem.
Answer:
The whole problem here can be traced to the transition from one slope to the other. Ice and water shield under the shingles at the transition point would do away with it but if the second slope is really gentle, you may end up with an ice dam that you might not want to be dealing with.