Question
David, Emma, Frank, and Grace need to cross a river. The only possible way to cross the river is a bridge that can only hold at maximum $2$ people at once. It's night time, so they can only cross the bridge using a lantern and they only have $1$ lantern. Each pair of people can only cross at the pace of the slowest person. All people need to get across as fast as possible. Their crossing times are as follows: David takes $10$ minutes, Emma takes $5$ minutes, Frank takes $2$ minutes, and Grace takes $1$ minute. What is the minimum time required for all of them to get across to the other side?