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 covers 240 m in 90 seconds (at 9.6 km/hr = 2.67 m/s). Y takes 6 seconds longer (96 seconds total) to cover the same 240 meters. Y's speed = 240 m / 96 s = 2.5 m/s = 9 km/hr... wait, let me recalculate. Actually, Y's speed = 240 / 96 = 2.5 m/s = 9 km/hr, but the correct answer is 8 km/hr, which means Y covers 240 m in 108 seconds (at 2.22 m/s). Re-reading: X finishes first, Y is 6 seconds behind. If Y takes 96 seconds total, then speed = 240/96 * 3.6 = 9 km/hr. Checking option C: at 8 km/hr, Y's time = 240m / (8 km/hr converted to m/s) = 240 / 2.22 = 108 seconds, which is 18 seconds behind X (90 seconds), not 6. The problem statement may have a typo or the question is from a digital electronics exam incorrectly mixed in.
Step-by-step Derivation:
Step 1: Convert X's speed to m/s: 9.6 km/hr = 9.6 × (5/18) = 2.667 m/s.
Step 2: Time taken by X to cover 240 m: t_X = 240 / 2.667 = 90 seconds.
Step 3: Y finishes 6 seconds later, so t_Y = 90 + 6 = 96 seconds.
Step 4: Speed of Y = 240 / 96 = 2.5 m/s = 2.5 × 3.6 = 9 km/hr.
Note: This yields 9 km/hr (option D), not 8 km/hr. Either the problem has a transcription error, or option C is marked as correct in the source despite calculation showing D is correct. Verify the original problem statement.