 Chapter 1

• The two trains need 30 minutes to meet, and the super visor makes 7km in 30 minutes, but he needs only 6,3km too reach the switch. That mean he will be there in time...

• Supervisor speed is 14 km/h = 35/9 m /sec

distance the switch is 6300m

arrived the switch a supervisor 6300/ 35/9 = 1620 sec= 27 min

A train move 160 km/h = 400/9 m/sec

until 1620 sec =(400/9)m*1620 = 72000m= 72 km

B train move 120 km/h = 100/3 m /sec

until 1620 sec = (100/3)m*1620= 54000m= 54km

27 min later A train are 72 km B train are 140-54km=86km

when the switch are between 72km and 86 km supervisor can save the trains

when the switch out the 72 km and 86 km distance , supervisor dont can save the trains

• Train A's speed is 160kmph, so it will cover 80kmph in half an hour.

Train B's speed is 120kmph, so it will do 60kmph in half an hour.

80km + 60km = 140km which is the distance between them at present; therefore they would crash in 30 minutes.

If the Conductor can run at an average speed of 14kmph (he's faster than me!), then he'll manage to run 7km in 30mins and reach the switch in time.

• Maths task: Yes he is in time to save the trains.

The trains are only 140 km away from each other.

The speed of train A is 160 km/h; the speed of train B is 120 km/h.

Summed speed is va +vb = 280 km/h.

Time to crash is 140 km / 280 km/h = 0.50 h

The manual switch is 6,300 metres away from the supervisor.

He runs at an average speed of 14 km/h, doing 6.3 km = 6.3 km / 14 km/ h = 0.45 h

That means he is just in time.

• yes the crash can be prevented, the trains will crash in 30 mins, he can get to the switch in 27 mins there by preventing the crash.

• Hij is op tijd.

Al had t niet veel langer moeten duren. 14 km/uur rennen = 233.33/minuut rennen.

6300 (meter) : 233.33 (meter/minuut) = 27 minuten.

In 27 minuten wordt met een snelheid van 14 km/uur dus 6300 meter afgelegd.

Trein A rijdt 160 km/uur. Dat is 160:60= 2.666 km/minuut.

Trein B rijdt 120 km/uur. Dat is 120:60=2.000 km/uur.

Trein A en B leggen samen dus 4.666 km/minuut af.

In 27 minuten leggen ze samen dus 4.666X27=125.982 km af.

Op het moment dat de supervisor na 27 minuten de schakelaar bereikt zijn de treinen nog 140-125.982=14.018 meter van elkaar verwijderd.

• Yes. He will arrive at the switch in 27 minutes((6.3km/14km)=.45 x 60 mins) which is 3 minutes before the crash. Train A will travel 72 km (160km x .45 hours) and Train B will travel 54 km(120km x .45 hours). They will still be 14 km apart.

• YES

120km/h + 160km/h = 280 km/h need 30 mintes for the 140km

Supervisor runs 14km in 1 hour = 7 km in 30 minutes

distance is 6.3 km which is less than the 7 km he can run

• yes.

convert the 6300 meters to kilometers and divide by 14km/h.

• at first sorry for my english...

speed of both trains is 160+120 = 280 km/h

so distance between trains will be over 140km / 280km/h = 0,5h and trains collise

supervisor have 0,5h to swap the manual switch, and he run 14km/h. within 0,5h he will reach 7 km, and the switch is on 6,3km, So he reaches the switch before the trains Collise and has 3 minutes to flip the switch

• Yes, he will make it in time to throw the switch.

How? Take the train speeds, add them together 160 km/hr plus 120 km/hr equals 280 km/hr. Since they are 140 km apart, divide 140 by 280 to get the amount of time until they collide. This means it is 30 minutes to collision.

Adams speed is 14 km/hr. So in 30 minutes, he can run 7 km or 7000 metres. Since the distance to the switch is 6300 metres, Adam makes it in time.

• Time until the 2 trains will meet/crash:

t1=d/(VA+VB) > t1=140/(160+120)=0.5h=30 min

Time the supervisor reaches the switch:

t2=d/Vc > t2=6.3/14=0.45h=27 min

t2<t1 > the supervisor has time to operate the manual switch.

• Yes he can stop both trains from colliding.

The two trains are approaching each other, since the gap is 140 km and they travel with a combined speed of 280 km/h, they would collide in 30 min. The supervisor can run 7 km in 30 min at average speed of 14 km/h. Therefore he can reach the switch which is 6.3 km away before the trains collide.

• The supervisor can stop the trains from colliding. He can run 7 km in 30 min and the switch is only 6.3 km away.

The trains would collide in 30 min, since they approach each other with 280 km/h and they are at the moment 140 km apart.

• the supervisor will be in time.

The teains' sum speed is 280km/h.

Time needed - 6.3/14=0.45h

At that moment the train will went 0.45×280=126km.

• Поїзди зустрінуться через 0,5 години (160х+120х=140 км, де х - час через який відбудеться зіткнення, 280х=140, х=0,5), а диспетчер добіжить до ручного керування через 0,45 години (6300 м / 14000 км/год= 0,45) - відповідно встигне попередити аварію.

• Yes, the supervisor will be in time to save the trains from collision.

It takes the supervisor 27 mins to reach the switch.

Train A will travel 72 kms in 27 mins

Train B will travel 54 kms in 27 mins

At that time, Train A will be 14 kms apart from Train B

• Ano, bude čas na záchranu vlaků.

Vlaky se potkají za 30 minut.

Vlaky: 160 km/hod. + 120 km/hod. = 280 km/hod.

140 km / 280 km = 30 minut (resp. 0,5 hod.)

Vedoucí urazí vzdálenost za 27 minut.

Vedoucí: 6,3 km / 14 km/hod = 0,45 hod = 27 minut

Yes, it will be time to save the trains.

Trains meet in 30 minutes.

Trains: 160 km/hr. + 120 km/hr. = 280 km/hr.

140 km / 280 km = 30 minutes (or 0.5 hours)

The supervisor travels the distance in 27 minutes.

Supervisor: 6.3 km / 14 km/hr. = 27 minutes (or 0.45 hours)

• Supervisor will run 6,3km at 14km/h for 27 minutes. Meanwhile the trains collides after 30 minutes. 30 minutes at 160km/h means 80km of distance. 30 minutes at 120km/h means 60km distance. 60 + 80 = 140

So, if the supervisor hits the button after 27 minutes - 3 minutes before the collision, the distance between the trains will be ca. 14km when they start breaking, so this is enough distance to stop both trains in time and to not collide each other. 