Start vs catch calculation: Two boys A and B run at 4.5 km/h and 6 km/h, respectively. Over a 1 km course, A has a 190 m start. By how many metres does B still win?
Aptitude
Races and Games
Difficulty: Medium
Choose an option
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A60 m
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B65 m
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C45 m
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D75 m
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E80 m
Answer
Correct Answer: 80 m
Explanation
Introduction / Context:With different speeds and a head-start, compute where the faster runner is when the slower finishes. The difference to the finish line is the winning margin.
Given Data / Assumptions:
- Course = 1000 m; A starts 190 m ahead → A needs 810 m.
- vA = 4.5 km/h; vB = 6 km/h; constant speeds.
Concept / Approach:Time for A to finish tA = distance / speed. In that time, B covers vB * tA. Compare B’s covered distance with 1000 m.
Step-by-Step Solution:
Convert speeds to m/s: vA = 4.5 * 1000 / 3600 = 1.25 m/s; vB = 6 * 1000 / 3600 = 1.666… m/stA = 810 / 1.25 = 648 sB's distance in tA = 1.666… * 648 = 1080 mWinning margin = 1080 − 1000 = 80 mVerification / Alternative check:Ratio method: In A's finish time, B covers (vB/vA) * 810 = (6/4.5) * 810 = (4/3)*810 = 1080 → margin 80 m.
Why Other Options Are Wrong:60/65/45/75 do not match the computed 80 m margin.
Common Pitfalls:Subtracting the 190 m head-start from 1000 m directly without applying speed difference.
Final Answer:80 m