Comprehension
A road network (shown in the figure below) connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and AC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long.
Mr. X and Mr. Y leave A at 08:00 am, take different routes to city C and reach at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y’s speed on segment DC is 55 km per hour.
Question: 1
What is the average speed of Mr. Y for the journey in km per hour?
What is the average speed of Mr. Y for the journey in km per hour?
Show Hint
In problems involving average speed, remember to calculate the total distance and the total time for the journey to determine the Correct Answer.
Updated On: Aug 5, 2025
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The Correct Option is B
Solution and Explanation
We are given that Mr. X and Mr. Y start at the same time and reach city C at the same time. Mr. X travels from A to B and then to C, while Mr. Y travels from A to D and then to C.
The total time taken by Mr. X is the time to travel from A to B and then from B to C. The time for Mr. X to travel from A to B is \( \frac{100}{61.875} = 1.615 \) hours.
To find Mr. Y's average speed, we use the total time taken by Mr. X and calculate the total distance traveled by Mr. Y.
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Question: 2
The total distance travelled by Y during the journey is approximately:
The total distance travelled by Y during the journey is approximately:
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In problems involving distance traveled at different speeds, break the journey into segments and calculate the distance for each one separately.
Updated On: Aug 5, 2025
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The Correct Option is C
Solution and Explanation
To find the total distance traveled by Mr. Y, we calculate the distance for each segment. The distance traveled by Y on segment AD is \( 45 \times t \), where \( t \) is the time taken. The distance on segment DC can be found using the given speed.
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Question: 3
What is the length of the road segment BD?
What is the length of the road segment BD?
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When the problem does not provide enough information to solve for a specific value, carefully check the given constraints and data.
Updated On: Aug 5, 2025
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The Correct Option is D
Solution and Explanation
The length of segment BD cannot be determined with the given information because we do not have sufficient data to calculate it directly from the provided distances and speeds.
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