Instructions
Read the following scenario and answer the THREE questions that follow.
Comprehension:
The diagram below represents a road network connecting five towns, namely Meereen, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown in the diagram. The straight road that connects Meereen to Gulltown passes through Oldtown. Another straight road, running west to east, connecting Meereen to Winterfell, passes through Lannisport. Further, two straight roads, one from Lannisport to Oldtown and another from Winterfell to Gulltown, are perpendicular to the road joining Meereen to Winterfell, and run from south to north.
Consider a car always travelling at the maximum permissible speed, and always taking the shortest route. It takes 1 hour to reach Oldtown from Meereen, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown. (For this problem, always consider the shortest route in terms of distance.)
Question 23.
Tyrion Lannister drove from Meereen to Oldtown, then from Oldtown to Lannisport, and finally from Lannisport to Winterfell, always taking the shortest paths. He always drove at a speed 10 km/hr below the maximum speed limits for the stretches he took. What was his total driving time closest to?
Question Explanation
We are told that a car always travelling at the maximum permissible speed, and always taking the shortest route takes 1 hour to reach Oldtown from Meereen, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown.
So, distance between Oldtown and Meereen is 100*1 = 100km
Distance between Gulltown and Oldtown is 25*2 = 50km.
Distance between Winterfell and Gulltown. is 120*3/4 = 90km.
Let the distance between Meereen and Winterfall be x.
Using the pythagoras theorem,
x = 120 km
For convience, we are refering the vertices as the starting letters of towns.
Using the similar triangle rule, MOL is similar to MGW.
So,
ML = 80 km.
LW = 40 km.
LO = 60 km
The path Tyrion Lannister took is MO, OL, LW.
Distances of these path are 100, 60, 40. The respective speeds are 90, 10, 110.
So, the total time taken will be
0.47 of an hour is 28 mins.
So, answer will be 7 hr 28 mins
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