NEED MATH HELP!?!? THIS IS DRIVING ME NUTS! ?

Question

Abe, Betty, Carlos, Darlene, Erica, and Frank need to cross a bridge. It is dark, they have one lantern between them, it is too dangerous for more than two to be on the bridge at once and no one can be on the bridge without holding onto the lantern. Abe can walk across the bridge in 45 minutes, Betty takes 65 minutes, Carlos takes 90 minutes, Darlene takes 115 minutes, Erica takes 130 minutes, and Frank takes 135 minutes. When two cross the bridge together they must both hold onto the lantern and it takes the time of the slower to get across. What is the least number of minutes it can take for all 6 to get across the bridge?

Answer 1

I'm no genius and this is probably wrong, but wouldn't you take the 3 longest times and add them together?

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No, I'm wrong.

It would be 315 minutes, I'm pretty sure.

Answer 2

1/2(6+4x) - 1/4(5x-12) = 1/2(7x-4)

= 6/2 + 4x/2 - 5x/4 + 12/4 = 7x/2 -4/2

after simplyfing it

= 3+2x-(5x/4)+3 = (7x/2)

= 2x-(5x/4)-(7x/2) = -2-3-3

= (8x-5x-14x)/4 = -8

= -(11/4)x = -8

= x =32/11  Answer  

Answer 3

45 65 90 115 130 and 135 are the times.

You want to double up the slowpokes as much as possible

and use the jackrabbits (relatively speaking) to bring the

lantern back as much as possible.

45 and 65 go across (65 mins used),

45 comes back (45 used)

135 and 130 go across (135 used)

65 comes back (65 used)

45 and 65 go across (65 used)

45 comes back (45 used)

90 and 115 go across (115 used)

65 comes back (65 used)

45 and 65 go across (65 used)

total:

65 + 45 + 135 + 65  + 65 + 45 + 115 + 65 + 65 = 665 minutes

(That is faster than everyone going with 45 and 45 coming back each time:

135 + 130 + 115 + 90 + 65 + 4 * 45 = 715 minutes.)

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