There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of C. E is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?
30 km
To find the distance covered by the person traveling from D to F, we first need to map out the positions of the seven places based on the given directions and distances.
Mapping the Locations
Let's establish the coordinates of each place relative to a starting point.
A and B: A is 6 km south of B. If we place B at (0, 6), then A is at (0, 0).
A and C: A is 10 km west of C. This places C at (10, 0).
C and D: D is 5 km east of C. Since C is at (10, 0), D is at (15, 0).
D and E: E is 6 km north of D. Since D is at (15, 0), E is at (15, 6).
B and F: F is 9 km west of B. Since B is at (0, 6), F is at (-9, 6).
F and G: F is 12 km north of G. Since F is at (-9, 6), G is at (-9, -6).
Calculating the Route from D to F
Based on the roads provided (AB, AC, CD, DE, BF, EG, and FG), we must find a connected path from D to F using only these specific road segments.
Segment 1: From D to C (Road CD)
Distance = 5 km
Segment 2: From C to A (Road AC)
Distance = 10 km
Segment 3: From A to B (Road AB)
Distance = 6 km
Segment 4: From B to F (Road BF)
Distance = 9 km
(Note: There is an alternative path through E, but E only connects to D and G, and G connects to F. However, the road EG connects E and G directly, but the road DC + AC + AB + BF is the most direct path utilizing the available roads.)
Total Distance Calculation:
$$\text{Total Distance} = \text{DC} + \text{CA} + \text{AB} + \text{BF}$$
$$\text{Total Distance} = 5 + 10 + 6 + 9$$
$$\text{Total Distance} = \mathbf{30\text{ km}}$$
Final Answer:
The distance covered by the person traveling from D to F is 30 km.
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