if a train runs at 40 kmph it reaches its destination late by 11 minutes, but if it runs at 50 kmph it is late by 5 minutes only. find the distance to be covered by the train . please explain this answer with process
Answers
Answer:
19 MINS
EXPLANATION:
Let the correct time for the train to complete the journey is x minuets
Then train cover distance in x+11 minuets at speed 40 km\hr = 40(x+11) km /60
Then train cover distance in x+5 minuets at speed 50 km\hr =
50(x+5) km /60
Both are same then :40(x+11) /60=50(x+5) /60
∴40x+440=50x+250
∴−10x=−190
∴x=19 minutes
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Answer:
20km
Step-by-step explanation:
Let 'd' be the distance travelled in km
also, Let the actual time required by the train to reach the destination in hours be t
Now,
Case 1
Distance = speed × time
According to the Question,
d = 40(t + (11/60)) ------- 1
Simplifying we get
d = (40t + (440/60)) -------- 2
Note:- I have divided the minutes by 60, this is because we took 11 as minutes and while dealing with km/h, we must change the time into hours
Case 2
According to the Question,
d = 50(t + (5/60))
Simplifying we get
d = 50t + (250/60) ------- 3
We know that the distance travelled by the train is same even if time and speed changes
then,
Eq.3 = Eq.2
that is,
50t + (250/60) = 40t + (440/60)
50t - 40t = (440/60) - (250/60)
10t = ((440 - 250)/60)
10t = 190/60
10t = 19/6
t = 19/60 hrs
we know,
1 hr = 60 minutes
then,
19/60 hrs = (19/60) × 60 = 19 minutes
so, it was supposed to arrive at the station after 19 minutes
But we must find the distance travelled,
Putting t = 19/60 in eq.1
d = 40((19/60) + (11/60))
d = 40((19 + 11)/60)
d = 40 × (30/60)
d = 40 × (1/2)
d = 40/2
d = 20 km
Thus the total Distance covered in km is 20km
Hope it helped and you understood it........All the best