Two men walked through the countryside toward another village. As they come to the edge of a river, they saw an old woman sitting there upset because the bridge was____by the storm, and she was too weak to walk across the stream. The first man said____, “We are tall enough, and we can carry you across” The second man thought it troublesome, but he agreed reluctantly（不情愿地）. So the two men ____ the bridge, lifted her between them and carried her across the river. When they got to the other side, they set her down and she went on her way gratefully. After they had walked another mile or so, the second man began to complain “My back began to hurt for lifting her.” The first man ____ smiled and nodded without a word.

三位同学准备进行爬楼比赛，看看谁的功率大。他们展开了如下的讨论：
甲：只有测出各自的体重、爬楼用的时间和爬楼的高度，才能进行比较；
乙：在爬楼的时间相同时，只要测出各自的体重、爬楼的高度，就可以进行比较；
丙：在爬楼的高度相同时，只要测出各自的体重、爬楼的时间，就可以进行比较。
正确的是（　　）

若集合$A=\left\{x|x^2-2x<0\right\},B=\left\{x|x>1\right\}$，则$A\cap B=$(  )