A, B and C are in a cycle race of 24,300 meters. A cycles twice as fast as B. C cycles at one-third the speed of B. C completes the race in 45 minutes. Then where was B from the finishing line when A finished the race?

1. A

   12144 m

2. B

   12150 m

3. C

   12148 m

4. D

   12155 m

Appeared in: DSSSB October 2024

Explanation

• The solution starts by calculating C's speed using the given distance (24,300 m) and time (45 min), which is 540 m/min.
• Using the relative speed information, B's speed is found to be three times C's speed (3 × 540 = 1620 m/min).
• Similarly, A's speed is twice B's speed (2 × 1620 = 3240 m/min).
• The time taken for A to finish the race is calculated by dividing the total distance by A's speed (24300 / 3240 = 7.5 minutes).
• In these 7.5 minutes, the distance B travels is calculated (1620 m/min × 7.5 min = 12,150 m).
• Finally, B's distance from the finishing line is the total race distance minus the distance B has covered (24,300 m - 12,150 m = 12,150 m).

Why Other Options Were Wrong

• Option A: This value is incorrect and likely arises from a miscalculation at one of the steps, such as determining the speeds or calculating the final distances.
• Option C: This is a numerical error. The precise calculation based on the given speeds and times does not yield this result.
• Option D: This value is incorrect. It does not match the calculated remaining distance for cyclist B when A finishes the race.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the application of fundamental concepts of speed, distance, and time, involving relative speeds and multi-step calculations as background academic context rather than a clinical decision trigger.
• This question tests foundational mathematical reasoning and calculation skills.
• While not a clinical scenario, the ability to perform multi-step calculations is crucial for nurses in tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data trends.
• Accuracy in calculation is a critical patient safety skill, as errors can have serious consequences in a clinical setting.

How to Approach the Question

• First, identify all the given variables: total distance, time for one person (C), and the relationships between the speeds of all three people (A, B, C).
• Use the known distance and time for C to calculate C's speed using the formula: Speed = Distance / Time.
• Use the speed of C and the given ratios to systematically calculate the speeds of B and then A.
• Once you have A's speed, calculate the time A takes to complete the full race distance.
• This time is the key. Use this duration to find out how far B traveled in the same amount of time (Distance = Speed of B × Time of A).
• Finally, subtract the distance B traveled from the total race distance to find B's distance from the finishing line.

Concept Tested & Keywords

• Concept Tested: This question tests the application of fundamental concepts of speed, distance, and time, involving relative speeds and multi-step calculations.
• Stem keywords: cycle race, 24,300 meters, twice as fast, one-third the speed, 45 minutes
• Lead-in keywords: where was B from the finishing line

Question ID

qF7x4VvzmyKBNfo0g2NOn

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