Four GE employees must make a trip to 3100 in order to help with an urgent repai

Question

Four GE employees must make a trip to 3100 in order to help with an urgent repair after hours. In order to comply with safety rules, only two of them may walk there at a time and whoever takes the trip must carry a cell phone. However, there is only one cell phone among them and they don’t all walk at the same pace. It takes the first person 2 minutes, the second person 4 minutes, the third person 14 minutes, and the fourth person 20 minutes. What is the fastest time that all four GE employees can arrive at 3100?

Explanation / Answer

"only two of them may walk there at a time" means 1 person at a time or 2 person at a time can make a trip.

"whoever takes the trip must carry a cell phone. However, there is only one cell phone among them "

As there is only one cell phone and person on trip musy carry it; is possible only when 1 person makes trip at a time.

there can be different cases about which person starts trip:

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Say second person goes first then time taken to reach at 3100 is 2 minutes

as second person is carrying cell phone so s/he must return cell phone back so that other employee can reach 3100 so time taken to go back at starting position is 2

so time taken by second person including return trip=4+4

similarly time taken by first person including return trip=2+2

similarly time taken by third person including return trip=14+14

time taken by fourth person to reach 3100=20

as all employee reached 3100 so no need to return back

Hence total time consumed by employees to reach 3100 =4+4+2+2+14+14+20=60

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say this time first person starts making trip and fourth person is the last trip maker

then total time consumed =2+2+4+4+14+14+20=60 min

using above pattern we see that time changes only due to Last person that completes trip so possible situations when time will be different are:

2+4+4+14+14+20+20=78 min

2+2+4+14+14+20+20=76 min

2+2+4+4+14+20+20=66 min

2+2+4+4+14+14+20=60 min

Hence the fastest time that all four GE employees can arrive at 3100 is 60 min

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