Question

The Bridge Problem

A group of four people has to cross a bridge. It is dark, and they have to light the path with a flashlight. No more than two people can cross the bridge simultaneously, and the group has only one flashlight. It takes different time for the people in the group to cross the bridge:

Chris crosses the bridge in 1 minute,

Tracy crosses the bridge in 2 minutes,

Ashley crosses the bridge in 5 minutes,

Jalen crosses the bridge in 10 minutes.



How can the group cross the bridge in 17 minutes?

Answer 1

So, the first thing is that the group requires flashlight to cross the bridge. It also means that each time one person must return to bring back the flashlight.

Chris and Tracy cross the bridge in 2 minutes. ( The maximum time required by both of them would be 2 minutes)

Then Chris would return with flashlight in 1 minute.

Ashley and Jalen then cross the bridge in 10 minutes.

Now, Tracy will return with flash light in 2 minutes.

Then, Chris and Tracy will cross the bridge in 2 minutes.

Total time taken => 2+1+10+2+2 => 17 minutes.

Hope this helps :)

Answer 2

Chris and Tracy cross the bridge together = 2 minutes

Chris goes back on his own (leaving Tracy across the bridge) = 1 minute

Chris gives the flashlight to Ashley

Ashley and Jalen cross the bridge together = 10 minutes

They give the flashlight to Tracy (who was waiting across the bridge)

Tracy goes back = 2 minutes

Chris and Tracy cross the bridge together = 2 minutes

Total 17 minutes