Respuesta :
Answer:
Shortest Path : A-C, C-Z
Shortest possible time = 143
Step-by-step explanation:
P.S - The exact question is -
Given -
T1 = 38
T2 = 52
T3 = 63
T4 = 67
T5 = 91
T6 = 62
T7 = 64
To find - What is the shortest path and what is the shortest possible time to travel from A to Z ?
Proof -
Choices for shortest path is -
Choice 1 : A-B, B-E, E-Z ;
Choice 2 : A-C, C-Z ;
Choice 3 : A-B, B-D, D-Z
Now,
For Choice 1 : A-B, B-E, E-Z
Distance between A-B = T1 = 38
Distance between B-E = T4 = 67
Distance between E-Z = T7 = 64
So,
The distance = 38 + 67 + 64 = 169
Now,
For Choice 2 : A-C, C-Z
Distance between A-C = T2 = 52
Distance between C-Z = T5 = 91
So,
The distance = 52 + 91 = 143
Now,
For Choice 3 : A-B, B-D, D-Z
Distance between A-B = T1 = 38
Distance between B-D = T3 = 63
Distance between D-Z = T6 = 62
So,
The distance = 38 + 63 + 62 = 163
∴ By comparing we get
Shortest Path = A-C, C-Z
Shortest possible time = 143
The shortest path is A→C→Z and the shortest possible time is 143 units option second is correct.
It is given that the traveler is trying to determine the fastest way to travel from city A to city Z.
It is required to find the shortest path and the shortest possible time to travel from A to Z.
What is the shortest path?
It is defined as the path in which all the sum of the path will be shortest in a weighted diagram known as the shortest path.
We have the time required to travel from A to B is T1 = 38 units
Similarly, for the path A to C is T2= 52 units
For the path B to D is T3= 63 units
For the path B to E is T4 = 67 units
For the path C to Z is T5 = 91 units
For the path D to Z is T6 = 62 units
For the path E to Z is T7 = 64 units
For the path A→B→E→Z
The total time required = T1+T4+T7
= 38+67+64 ⇒169 units.
For the path A→C→Z
The total time required = T2+T5
= 52+91 ⇒143 units.
For the path A→B→D→Z
The total time required = T1+T3+T6
= 38+63+62 ⇒ 163 units.
Thus, the shortest path is A→C→Z and the shortest possible time is 143 units option seconds is correct.
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