17 mins
1: Rachel(1) and Ben(2) walk across the bridge
2: Rachel(1) walk back to the same side
3: George(7) and Yvonne(10) walk across the bridge
4: Ben(2) walk back to another side of the bridge
5: Then Ben(2) and Rachel(1) walk across the bridge
Strategy 1
Person A = 1
Person B = 3
Person C = 5
Person D = 7
1: Person A + D walk across together
2: Person A walk back to the same side
3: Person A + C walk walk across together
4: Person A walk back again
5: Person A + B walk to another side
= 17 mins
Strategy 2
Person A = 1
Person B = 3
Person C = 5
Person D = 5
1: Person C+D walk across
2: Person C walk back
3: Person C+B walk across
4: Person B walk back
5: Person A+B walk across
= 21 mins