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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?

Answer 1

William Audy

#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")#.

It must travel 1.5 kilometers in order to pass the train.

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

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

#sf((b))#

The distance the car travels in relation to a stationary observer is given by:

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

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Answer 2

Parker Abbott

Time to pass the train: 9 minutes.
Distance traveled by the car in that time: 13.5 kilometers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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?

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?