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?

Question

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?

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Answer 1 · 2016-10-21T03:44:22

#sf((a))#

#sf(4.5color(white)(x)"min")#

#sf((b))#

#sf(6.75color(white)(x)"km")#

#sf((a))#

The velocity of the car relative to the train = #sf(90-70=20color(white)(x)"km/hr")#.

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

#sf(t=d/v=1.5/20=0.075color(white)(x)"hr")#

#sf(t=0.075xx60=4.5color(white)(x)"min")#

#sf((b))#

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

#sf(d=vxxt=90xx0.075=6.75color(white)(x)"km")#