trains chapter shortcuts in arthematic
Answers
There are 5 types of problems .
#1. Type 1:
BASED ON TIME, SPEED AND DISTANCE WITH TYPE CONVERSION:
A train covers a distance of 936km in 13 hours. What is the speed of the train express in m/sec?
Explanation:
Speed=Distance/time
=936/13
Speed =72km/hr
Type Conversion (km/hr m/sec):
=72*(5/18)
# .2 TYPE 2:
BASED ON LENGTH:
1. If the train cross a bridge whose length is 600m and cross a pole in 48sec when it travels at the velocity of 36km/hr.Then how long will it take to cross a stationery train whose length is twice the length of the moving train?
Explanation:
Bridge(600m)
36km/hr is converted to m/sec 36*(5/18)=10m/sec.
Length=Speed*Time=48*10=480m.
Stationary train whose length is twice that of moving train =2(480)=960m
Time taken to cross a stationary train=Distance/Speed=(960+480)/10=1440/10=144sec
#. 3 TYPE 3:
BASED ON TRAINS REACHING LATE AND EARLY:
If a train runs at 40km/hr, it reaches its destination late by 11 minutes but if it runs at 50km/hr. It is late by 5mins only. The distance travelled by the train is?
Explanation:
LCM 40,50=200KM
Let it usually reach at 9AM
Time =Distance/Time
Distance Speed Time
200 40 5hr
200 50 4hr
5hrs -4hrs=1hr =200km
9.11AM -9.05AM=6 min=20km
2.If a train runs at a rate of 60km/hr, it reaches its destination early by 30 min and if it runs at a rate of 40 km/hr then it reaches 30mins late Then what is the distance travelled by the train?
Explanation:
LCM 60,40=60KM
Let its correct time =9AM
Distance Speed Time
60km 60km/hr 1hr
60km 40km/hr 1hr30min
1hr 30min – 1hr =30min=60km
#.4 TYPE 4:
BASED ON AVERAGES:
1.When a train travels from Delhi to Mumbai at the rate 120km/hr and return back at the rate of 180km/hr then what is the average speed of the train?
Solved Problem
Average Speed=2*120*180/(120+180)
=144km/hr
2.The train covers the certain distance at the rate of 20km/hr,120km/hr and 60km/hr then what is its average speed?
Explanation:
Average Speed when 3 speeds are given:
=(3*20*120*60)/((20*120)+(120*60)+(20*60))
Average Speed=40km/hr.
#.5 TYPE 5:
BASED ON DIRECTION:
1.A train starts its journey from Mumbai to Goa with a speed of 120km/hr and another train moves in same direction whose velocity180km/hr. Find the difference between them after travelling 5hrs?
Explanation:
A(180km/hr) , B(120km/hr) Same Direction(180-120=60)
After travelling 5hrs it can cross 60*5=300km
2.One local and another express train were proceeding in the same direction on parallel tracks at 29km/hr and 65km/hr respectively.The driver of the former noticed that it took exactly 16s for the faster train to pass by him.What is the length of the faster train?
Explanation:
Speed 1 Speed 2 Relative Speed (Same Direction)
29km/hr 65km/hr 65-29=36km/hr
Type conversion:
36km/hr 36*(5/18)=10m/sec
HOPE IT HELP YOU