a good train leaves a station at 6pm followed by a express train which leave at 8pm and travel 20km/hr faster than the goods train .The express train arrives at a station 1040km away .36 min before the goods train.Asuming the speed of both the train remain constant between the two station calculate the speed.
Answers
Let the speed of the goods train be
'x' km/hr
Then, speed of express train=(x+20) km/hr
Goods train leaves a station at 6pm and express train leaves the station at 8pm
also express train reaches its destination 36min before goods train.
We known that,
Time taken = distance covered /speed
Total distance=1040km
Time taken by goods train to cover
1040 km=1040/x
Time taken by express train to cover 1040 km=1040/(x+20)
As per given condition we have,
1040/x=1040/(x+20)+2(36/60)
1040/x-1040/(x+20)=2(3/5)
(1040x+20800-1040x)/(x²+20x)=13/5
13x²+260x=104000
x²+20x-8000=0
x²+100x-80x-8000=0
x(x+100)-80(x+100)=0
(x-80)(x+100)=0
x=80 (or) x=-100
Here x>0
Therefore x=80
Hence speed of goods train=80 km/hr
and speed of express train=100 km/hr.
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Let the speed of goods train be x km/hr. So, the speed of express train will be (x + 20) km/hr. Distance = 1040 km We know: Time = distance/speed Time taken by goods train to cover a distance of 1040 km = 1040/x hrs Time taken by express train to cover a distance of 1040 km = 1040/(x+20) hrs It is given that the express train arrives at a station 36 minutes before the goods train. Also, the express train leaves the station 2 hours after the goods train. This means that the express train arrives at the station (36/60 + 2) hrs = 13/5 hrs before the goods train.
∴ Total time taken by express train
t e =tt −2− 36/60
x+20/1040 = x/1040
−
60
120+36
x+20
1040
−
x
1040
=−
5
13
On solving the above, we get
x
2
+20x−8000=0
∴x=−100 or x=80
Since speed cannot be negative, x=80 km/hr
Speed of goods train is 80 km/hr and speed of express is 80+20=100 km/hr.
Since, the speed cannot be negative. So, x = 80. Thus, the speed of goods train is 80 km/hr and the speed of express train is 100 km/hr.