Calculate the shortest possible time to cross a bridge

Question
Maggie, Sam, Reed, and Jeff are on one side of bridge and they want to all make it to the other side in 17 minutes. It takes Maggie 10 minutes to cross, Sam 5, Reed 2, and Jeff 1. Only 2 people can walk across at a time and there is one flashlight. The flashlight has to be each person or group, and it has to be walked across, not tossed. Can it be done in 17 minutes?
Solution
First determine the fastest of the four. Jeff is the fastest who can cross the bridge in just a minute. Hence, use Jeff to walk back and forth of the bridge carrying the flashlight.
Second, identify pairs.

1. Maggie and Jeff
2. Sam and Jeff
3. Reed and Jeff
   

Third, compute the time spent by each pair and the time spent by Jeff going back to the foot of the bridge
Pair/Person Time (in minutes)
Maggie and Jeff 10 ===========> Maggie's time*
Jeff 1
Sam and Jeff 5 ===========> Sam's time*
Jeff 1
Reed and Jeff 2 ===========> Reed's time*
*Although Jeff can walk much faster, he can not leave any of his companions in the middle of the bridge with no light.



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