Mr. Woody Allen is standing at one of the three entrances (A) of a 5 story Manhattan Mall.
He needs to go from A to the other end (small shop) on the 4th floor at location (X). Ground floor is First floor in US.
And he hates malls so he wants to get there as fast as possible.
What is the fastest way (timewise) for Mr. Allen to get from A to X?
Provided below is the schematic of the Mall-not to scale. The Mall has 5 floors, each one 20 units tall. A, B and C are the 3 entrances. Distances are shown. Means of transportation and speeds are as follows:
Walking: Mr. Allen walks at an average speed of 1 unit per second and he also has average speed of 1 step (up or down) per second Stairs: There are 2 stairs. The Staircase at entrance A and at location E (50 units away from entrance C). Each staircase goes all the way to the fifth floor. There are 30 steps per floor (120 steps total). You can get on or off on any floor.
Mr. Allen has an average speed of 1 step per second (up or down). However, it is easier for him to go down the stairs so he is one second faster per floor going down.
Escalators: There are 3 Escalators all starting at the ground (first) floor.
Escalator 1 starts at location F (100 units away from A) and ends on the third floor at location H (66 units away from the stairs) YOU CANNOT GET OFF ON THE SECOND FLOOR.
Escalator 2 starts at location G (140 units away from A) and goes to fifth floor to location T, where you can get off. YOU CANNOT GET OFF ON ANY OTHER FLOORS (EXCEPT FIFTH OF COURSE).
Escalator 3 starts at location B (at the second entrance) and goes to the THIRD floor to location Z which is 125 units away from the stairs at E3. AGAIN THE ESCALATOR DOES NOT STOP ON THE SECOND FLOOR. All escalators run at a speed of 1 unit per second.
Automated Walk-ways (like you see at the airport): There are 2 of them. The one on the 4th floor goes from the middle point of the building M to the end X. IT DOES NOT HAVE EXIT ANYWHERE IN BETWEEN. ONCE YOU ARE ON IT, AT M, YOU MUST GO TO X. Of course he can walk next to the walk-ways in either direction. This Walk-way MX is slower and runs at 0.5 units per second
The second automated Walk-way starts at one end of the building (L) on the fifth floor and goes all the way to the other end of the building (O) –the whole 500 units. YOU CAN ONLY GET ON OR OFF AT L, N (MIDDLE OF THE BUILDING) OR AT O. This Walk-way LNO is faster and runs at 1 unit per second.
Elevators: There are 2 of them IK and DQ. IK goes from Floor 3 to 4 to 5 (or back) and is 100 units away from end of the building.
DQ goes from Ground floor to the 5th floor and stops at every floor. It is 20 units away from the middle point B.
The elevators run at a speed of 10 seconds per floor. But you must add 10 seconds additional (TOTAL, not per floor) for door openings and closings. So if Mr. Allen takes the elevator for 2 floors the total time will be 20+10=30 seconds.