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A car is moving on a highway at $$34\text{ m/s}$$. A man is standing by the side of the highway a long distance ahead of the car. Car sounds its horn for a $$5\text{ s}$$ duration. The car passes the man sometime after the horn is sounded. Find the length of time (in s) during which the man hears the sound of the horn. (Speed of sound is $$340\text{ m/s}$$.)
Correct Answer: 4.5
Let the car be at distance $$d$$ when the horn starts; that sound reaches the man at $$\frac{d}{340}$$. When the horn stops, 5 s later, the car is $$34 \times 5 = 170\text{ m}$$ closer, so the last sound reaches him at $$5 + \frac{d - 170}{340} = \frac{d}{340} + 4.5$$. He hears the horn for $$4.5\text{ s}$$.
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