In a 240 meters race X beats Y by 6 seconds.
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In a 240 meters race X beats Y by 6 seconds. The speed of X is 9.6 km/hour. Find the speed of Y.
Show answer & explanation
X finishes 240m in time t = 240m ÷ (9.6 km/hr converted to m/s) = 240 ÷ 2.667 ≈ 90 seconds. Y takes 90 + 6 = 96 seconds to finish the same 240m distance. Speed of Y = 240m ÷ 96s = 2.5 m/s = 2.5 × 3.6 = 9 km/hr... Wait, let me recalculate: 240 ÷ 96 = 2.5 m/s = 9 km/hr. Actually, checking option C (8 km/hr = 2.222 m/s): time = 240 ÷ 2.222 ≈ 108 seconds, difference = 108 - 90 = 18 seconds (not 6). Let me verify: 9.6 km/hr = 9.6/3.6 = 2.667 m/s; time for X = 240/2.667 = 90 sec. If Y's speed is 8 km/hr = 2.222 m/s, time for Y = 240/2.222 = 108 sec, difference = 18 sec. For a 6-second difference: Y's time = 96 sec, so Y's speed = 240/96 = 2.5 m/s = 9 km/hr (Option D). However, re-examining: perhaps the question means Y is 6 seconds behind when X finishes—this would give 9 km/hr. The provided answer key suggests C, but mathematically it should be D unless there's a different interpretation.
Step-by-step Derivation:
Step 1: Convert X's speed to m/s: 9.6 km/hr = 9.6 ÷ 3.6 = 2.667 m/s
Step 2: Calculate time for X to finish 240m: t_X = 240 ÷ 2.667 = 90 seconds
Step 3: Y is 6 seconds slower, so t_Y = 90 + 6 = 96 seconds
Step 4: Calculate Y's speed: v_Y = 240 ÷ 96 = 2.5 m/s
Step 5: Convert to km/hr: 2.5 × 3.6 = 9 km/hr
Note: Based on standard race problem interpretation, the answer should be D (9 km/hr). Option C (8 km/hr) would result in an 18-second gap, not 6 seconds.