# 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?

## 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. If the train's speed is 70 km/h, (a) how long does it take the car to pass it, and (b) how far will the car have traveled in the time?

Oct 21, 2016

$\textsf{\left(a\right)}$

$\textsf{4.5 \textcolor{w h i t e}{x} \text{min}}$

$\textsf{\left(b\right)}$

$\textsf{6.75 \textcolor{w h i t e}{x} \text{km}}$

#### Explanation:

$\textsf{\left(a\right)}$

The velocity of the car relative to the train = $\textsf{90 - 70 = 20 \textcolor{w h i t e}{x} \text{km/hr}}$.

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

$\textsf{t = \frac{d}{v} = \frac{1.5}{20} = 0.075 \textcolor{w h i t e}{x} \text{hr}}$

$\textsf{t = 0.075 \times 60 = 4.5 \textcolor{w h i t e}{x} \text{min}}$

$\textsf{\left(b\right)}$

Relative to a stationary observer the distance the car travels is given by:

$\textsf{d = v \times t = 90 \times 0.075 = 6.75 \textcolor{w h i t e}{x} \text{km}}$