A traveler is trying to determine the fastest way to travel from city A to city Z. The possible travel routes, with the time required for each segment, is shown below.
What is the shortest path and what is the shortest possible time to travel from A to Z? (Round your answer to the nearest whole number.)
Shortest Path Choices: A-B, B-E, E-Z ; A-C, C-Z ; A-B, B-D, D-Z
Answers
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.
Learn more about the shortest path here:
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Solution
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Step-by-step explanation:
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0: 0/1
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1. 1/-[infinity]
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Answers
Step-by-step explanation:
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18. 1 - [infinity] = -∞
19. [infinity]/0 = DNE
20. inf - inf = ∞