Three people (A, B, and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. There is also a bicycle available and any person can cross the bridge in 1 minute with the bicycle. What is the shortest time that all men can get across the bridge? Each man travels at his own constant rate.
(a) 2.75 minutes (b) 2.87 minutes (c) 2.92 minutes (d) 2.96 minutes

• A's speed is 1/10 (in bridges per minute), B's speed is 1/5, C's speed is 1/2, and the bicycle's speed is 1.
  The fastest way to get everyone across is for B and C to start out on foot and A to start out with the bicycle. At a point y, A will get off the bicycle and walk the rest of the way. Eventually C will get to the bicycle abandoned by A, then ride back to a point x, leaving the bicycle there, then turning around and walk until he reaches the end. Person B will walk until he reaches the bicycle left by C and then ride the rest of the way.
  Below are the times that each will take to cross, in terms of x and y:
  A: 1*y + 10*(1-y)
  B: 5*x + 1*(1-x)
  C: 2*y + (y-x) + 2*(1-x)
  Next equate these equations: 10 - 9y = -3x + 3y + 2 = 4x + 1.
  To solve set up two linear equations:
  10 - 9y = -3x + 3y + 2 -> 3x - 12y = -8
  10 - 9y = 4x + 1 -> 4x + 9y = 9
  Then solve for x and y:
  x = 12/25, y=59/75.
  Given these points it will take each person 73/25 = 2.92 minutes to cross. Since they all start and end at the same time, the total duration to cross the bridge is also 2.92 minutes.
  
• 11 years agoHelpfull: Yes(22) No(3)
• 2.92 minutes
• 11 years agoHelpfull: Yes(1) No(4)
• please explain..
• 9 years agoHelpfull: Yes(1) No(0)
• 2.92 minutes
  
• 11 years agoHelpfull: Yes(0) No(3)