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How far will the car have traveled in that time?

An automobile traveling 90 km/h overtakes a 1.5-km-long train traveling in the same direction on a track parallel to the road. The train speed is 70 km/h, – how long does it take the car to pass it – how far will the car have traveled in that time?

Answer:
\((a)\)
\(4.5 \mathrm{~min}\)
\((b)\)
\(6.75 \mathrm{~km}\)

Explanation:
\((a)\)

The velocity of the car relative to the train = \(90-70=20 \mathrm{~km} / \mathrm{hr}\)

To pass the train it needs to cover a distance of 1.5 km.

\(\mathrm{t}=\frac{\mathrm{d}}{\mathrm{v}}=\frac{1.5}{20}=0.075 \mathrm{hr}\)
\(\mathrm{t}=0.075 \times 60=4.5 \mathrm{~min}\)
\((b)\)
Relative to a stationary observer the distance the car travels is given by:
\(\mathrm{d}=\mathrm{v} \times \mathrm{t}=90 \times 0.075=6.75 \mathrm{~km}\)

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