 # Chapter 1

• yes he will be on time

runner needs 0.45h to get there (6,3/14)

Train A does in these 27 min: 72 km (0.45* 160)

Train B does 54 km (0.45*120)

and they would collide on 30 min: 140 km = x. 160 +x 120 --> X =30

supervisor has 3 min (unknown if that is enough to manually switch of course after the running)

• if the supervisor runs to the manual switch that is 6.300 metres away with a speed of 14 km/h he will be there at 27 mins.

train A in 27 mins will be managed to cover 72 km with a speed of 160 km/h.

train B in 27 mins will be managed to cover 54 km with a speed of 120 km/h.

that means that trains will be already covered the distance of 126 km between them and the wiill still having 14km remaing distance to each other from the 140 km that they had in first place.

So yes the supervisor will manage to stop the accident and save the trains!!!

• The two trains have a combined closure speed of 280kmh (160+120) so it will take them 30 minutes to cover 140km.

In 30 minutes the supervisor can run 7km, so he will cover 6,300m in less than 30 minutes (actual time = 27 minutes), which means he will be in time to throw the switch.

• Yes. The trains will crash in 30 minutes, and it will take 27 minutes for the superviser to get there. Phew!

• yes

the trains speed is 160+120km/h =280km/h they will meet in 30 min

The supervisor runs 7km in 30min =he will have 3 minutes to switch

• All trains and supervisers have ATW"s (audible track warning devices) common word is detonaters. the nearest train is over 140 kilometres away, if the superviser had 50 minutes walking time assuming the nearest train was doing 160kph the answer is yes he would have enough time, even to pause and place one ATW at 1200 metres one ATW at 2400 metres and 3 ATW's 10 metres apart at 3600 metres. this alone would be sufficient to stop any Train in the required distance before the switch. MY ANSWER IS YES HE WOULD MAKE IT IN TIME the superviser would have time for a cup of tea too

Yes. He will be in time to save the trains.

Explanation:

There two options.

Explation option 1:

The trains are on the same direction and Train B is ahead of Train A and because Train A speed is higher than Train B speed they will colide.

In this way Train B speed - Train A speed is of 40 KM/h. With this difference of speed the distance of 140 km between the two trains will be reached in 3.5 hours. So the operator has 3.5 hours until the collision.

The operator needs to run to the manual switch that is at a distance of 6300 meters that is equal to 6.3Km

Considering the operator runs at a constante pace of 14km/h in a distance of 6.3Km he will need 0.45hours to reach the manual switch.

Conclusion of option 1: we has a lot of time.

Explanation option 2:

The trains are on opposite directions.

Considering the operator runs at a constante pace of 14km/h in a distance of 6.3Km he will need 0.45hours to reach the manual switch.

Trains A at a constante speed of 120Km/h will travel in thoose 0.45 hours the distance of 54Km towards Trans B.

Trains B A at a constante speed of 160Km/h will travel in thoose 0.45 hours the distance of 72Km towards Trans A.

Therefore the total distance travelled by Train A and Train B until the operator reach the manual switch is 54Km + 72Km = 126Km.

But they have a total distance of 140Km therefore the operator has enough time.

• yes, trains will meet in 30 Minutes ((160+120)/140). Supervisor can run 14/2=7 km in half an hour, which is more than 6300 meters.

• Yes, supervisor saves the trains.

His journey takes 27 minutes and that's enough. The trains will be 14 km away.

Explanation:

As train A covers 160 km in an hour, it will cover 80 km in half an hour.

As train B covers 120 km in an hour, it will cover 60 km in half an hour.

After 30 minutes both trains will have approached by 140 kms (80km + 60km).

As the supervisor notices the problem when the trains are 140 km away from each other, he will have exactly 30 minutes to reach the switch.

As the supervisor can run at 14km/h, it will cover 700 meters in 3 minutes.

Then, it will take him 27 minutes to run 6300 meters (3 * 6300 / 700).

Consequently, he will reach the switch 3 minutes before the trains crash.

I hope the trains have a good braking system.

• yes

trains collide in (160+120)/140=0.5 h

he goes 0.5X14=7km > 6,300m in the time

• Łączna prędkość pociągów to 280 km/godz.,więc do zderzenia dojdzie za 30 min.Nadzorca jadąc ze średnią prędkością 14 km/godz w ciągu 30 min.przejedzie 7 km a z tego wynika że zdąży zapobiec katastrofie.

yes, he will be in the time to save the trains

2) explanation:

speed train 1 -> v1 = 160km/h; distance train 1 -> s1 = ?

speed train 2 -> v2 = 120km/h; distance train 2 -> s2 = ?

distance -> s = 140km

v = s/t -> t = s/v

t1 = s1 / v1 and t2 = s2 / v2

As the trains go against each other, they will go for exact the same time to the collision -> t1 = t2

And they go together the distance of s => s = s1 + s2

t1 = t2 = t

s1 / v1 = s2 / v2 // s1 = s - s2

(s - s2) / v1 = s2 / v2

- - - - - - - - - - - - - - -

s2 = (v2s) / (v1 + v2)

s2 = (120 x 140) / (160 + 120)

s2 = 60km

t = s2 / v2

t = 60 / 120

t = 0,5h -> time to collision

speed supervizor -> v3 = 14km/h

distance to switch -> s3 = 6,3km

t3 = s3 / v3

t3 = 6,3 / 14

t3 = 0,45h -> time to switch

If the time to switch is shorter as the time to collision, the trains will be stopped before the collision • Yes he will be in time..

Trains will take 30 mins to collide 0.5 hours.

Supervisor at 14km/hr will take 0.45 hours to reach the switch

160km/h +120km/h + 280km/h closing speed... over 140 km means 0.5 hours to collision

14km/h = 14000 meters per hour. 6300 metres devided by 14000 = 0.45

• The supervisor travels at 14km/h.

He needs to travel a distance of 6.3km.

6.3/14 = 0.45 hours to travel this distance.

The two trains travel at 160km/h & 120km/h.

This is a closing velocity of 280km/h.

They are 140km apart.

140/280 = 0.5 hours until the collision.

As long as the supervisor is not a government worker and actually does his/her job, the trains will be stopped prior to the collision.

• Yes, he will be in time. The supervisor needs (6,3/14) x 60 = 27 minutes to reach the switch.

In these 27 minutes, train A travels (27/60)x 160 = 72 km and train B travels (27/60) x 120 =54 km. In total, they travel 126 km while they are 140 km apart from each other. There is approximately 2 minutes left to turn the switch.

• yes he will.

Train a will travel 80 km in 30 mins

Train B will travel 60 km in 30 mins thereby the distance of 140km is covered . Assuming the switch is at this point on the track, the supervisor running at 14000 m/ h will cover 6300 meters in 0.45 hrs, which is less than the 0.5 hrs to the train collision.

regards No1 Engineer.

• yes, because he will reach the switch in 27 minutes, while the trains will collide in 30 minutes

• Yes.
Train A's speed every minute is 2.67Km and Train B's Speed per minute is 2 km
If the trains travel at a constant velocity the distance between them decreases by 46 km every 10 minutes
after 30 minutes the distance between them is less than 2 km

If the supervisor is traveling at 14 km/h he will run 7 km in half an hour, so he will reach 6,3 km in less than 30 minutes. Therefore by the time he reaches the switch the trains will be 2 km apart

• yes he will make it

trains will take half an hour to collide since the both approach at 280km/h and the distance is 140km.

at the speed of 14km/h it will take less than half an hour to cover the distance of 6300m

and have time to turn the switch