# Chapter 1

• Hello

Yes he can save the trains.

If he runs with a speed of 14km/h, he will make the 6300metres in 27 min.

6300metres/(14km/h / 60min) = 27min

In 27 min train A will go 72km and train B will go 54km, so the will be 14km apart from each other.

Train A (160km/h / 60min) x 27min = 72km

Train B (120km/h / 60min) x 27min = 54km

• He will make it, the trains will not crasch.

First train goes 80 km in 30 minutes

Second train goes 60 km in 30 minutes

=> so they will crash in 30 Minutes because 140km distance is done.

The supervisor runs 14 km/h so he reaches the switch in less than 30 Minutes, because he runs 7 km in 30 Minutes and he only needs 6,3 km.

So if the switch is located in the space left between the trains in the few minutes before they crash the supervisor can change the switch.

• Trains meet in 1 hour, Supervisor should reach the switch in 45 Min, so yes

• A kilometer is a 1000 meters, so in about 30 minutes he will be at the switch, so yes he can do it.

Thank you

Preston's Trains

Regards,

Eilenberg

DE201 & COM203

## Images

• the supervisor will be able to stop the trains in time.

If he runs at 14km/h it will take him around 27 min to reach the switch

train A runs at 160km/h, 44.44m/sec and train B at 120 km/h, 33.33m/sec

each second the two trains close each other with 77.77m

since they are 140km apart at the start, it would take them around 30 minutes before colliding

• Yes he can stop them, if he runs at 14 km, he will cover 7,000 meters and the trains are only 6,300 apart.

• two trains at closing speed of 280km/h distance is 140 km time to collision is 30mins

140*60/280 = 30mins

Supervisor is 6.3km from switch running at 14km/h is 27 mins from switch

6.3*60/14 = 27mins

So supervisor will get to the switch 3 minutes before the trains collide.

• No. Trains will meet in 1 hr. it will take the Supervisor 2.2 hrs to get to the switch.

• The trains are closing with one and other at 160+120=280km/h, the distance between them is 140km so they will hit each other in 30 minutes (140km/280km/h=0.5h) In 30 minutes the supervisor can run 7km (14km/h*0.5h=7km) 6.3km is less than 7km so he gets there on time to stop the crash.

• Yes, the supervisor will be able to save the trains.

It will take him 0,45 hour to get to the switch (6,3/14=0,45).
Train A will pass 72 km in 0,45 hour (160*0,45).

Train B will pass 54 km in 0,45 hour (120*0,45).
Together, they will pass 126 km - so on 140 km distance, there is 14 km difference - hence the trains wont collide.

• Yes.

He can cover the 6300m in 27 minutes at 14 km/hr. Train A will cover 72 km in 27 min at 160 km/hr. Train B will cover 54 km in 27 min. 72 + 54 = 126 km the two trains will cover in 27min which is less than 140 km they are from each other at start. When he reaches the switch, the two trains will not have yet collided.

• Both trains are running towards each other, so you have to add both of their speeds to have the total speed that covers the 140 km.

280 km/h to cover 140 km = 30 min left before collision.

Now if he runs at 14km/h, he will cover 7km in that time. The switch is closer than that, so yes he will succeed but just barely.

en pause indéterminée - away from the game until next interesting server

Likely coming back for clash!

• Addendum 2: looking carefully at the previous addendum, I created a paradox, suppose the observer would actually take (a very little more than) 30min to reach the switch. Then for the observer would see a collision, but the trains won't... absurd.

The solution to this paradox is that I assumed that in the frame of each train, the observer starts running at the same time as the trains are 140/γ km apart. However simultaneity is not conserved between different frames, thus the observer would then start running and see the trains 140km apart at different times.

• Yes, he could be there in 27 minutes = 1620 sec

Meanwhile

train 1 goes foreward 44.44 m/sec - 72 km in 27 minutes aprox.

train 2 goes foreward 33.33 m/sec - 54 km in 27 minutes aprox.

72+54 = 126

he could be there and the trainst still 14 km away from eachother

• Yes. The trains will crash in 1 hour and it will take the supervisor 1/2 t get to the switch.

• This is the solution and explanation

The supervisor makes it on time

## Images

• Impossible to say – it depends where the switch is located. Eg if 10m in front of either train.

Supervisor will reach the switch in 27mins ((6300/1000)/14x60)

Trains will cover the 140 miles and collide in 30mins (140/(160+120)x60)