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A train travels at an average speed of 90 km/hr without any stoppages. However, its average speed decrease to 60 km/hr on account of stoppages. On an average, how many minutes per hour does the train stop?
(A) 12 minutes
(B) 18 minutes
(C) 20 minutes
(D) 24 minutes
(E) 30 minutes
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(A) 12 minutes
(B) 18 minutes
(C) 20 minutes
(D) 24 minutes
(E) 30 minutes
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Bunuel
In 1 hour, the train travels 90 km (if there are no stoppages).
But in 1 hour, it actually travels only 60 km i.e. 2/3rd of the distance. So actually it runs for only 2/3rd the time i.e. 40 mins. So it stops for 20 min per hour on average.
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General Discussion
Bunuel
in 60 minutes the train is supposed to travel 90 km without stoppages
actually, in 60 minutes the train travels 60 km with stoppages i.e. 30 km less
with average speed 90 km/hr, the time taken by train to travel 30 km = 30/90 = 1/3 hours = 20 minutes
i.e. Train stops for 20 minutes every hour
Answer: Option C
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Bunuel
distance travelled @90kmph = 90 km and at 60kmph = 60 km ; difference in distance = 90-60 ; 30 km
@90kmph the distance of 30 km ; time would be would be 30/ 90 = 1/3 hrs or 20 mins
IMO C
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Actual Speed of the train = 90 KM/Hr = 1.5 KM / Min
Distance Travelled = 60 KM, Speed = 1.5 Km / Min, hence time = 60/1.5=>40 Mins
Halt Minutes = 60 - 40 =>20 Mins
Distance Travelled = 60 KM, Speed = 1.5 Km / Min, hence time = 60/1.5=>40 Mins
Halt Minutes = 60 - 40 =>20 Mins
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Don't we need to assume for that answer that we can ignore the deceleration of the train when arriving at a stop?
Let's say the distance the train travels is D kilometers. Thus, with stoppages it takes D/60 hrs and without stoppages it would have taken D/90 hrs. So for a D/60 hour trip, the train loses D/180 hrs (D/60 - D/90). Therefore, the time lost PER HOUR due to stoppages is:
(D/180)/(D/60)=1/3 hrs=20 minutes. Ans: C
(D/180)/(D/60)=1/3 hrs=20 minutes. Ans: C
Bunuel, can you please confirm the below thought process?
Avg Speed (w/ stops) = Distance / Total Time = 60 km/hr
Distance = (90 km/hr)(t1 hr) + (0 km/hr)(t2 hr) (km)
Total Time = t1 + t2 (hr)
Solve to get
t1/t2 = 2hr/1hr
In order to Avg 60 km/hr you need 2 hrs of 90 km/hr for every 1 hour the train is stopped (0 km/hr)
OR
1/3 of every hour = 20 minutes stopped C, 40 minutes running at 90 km/hr
Avg Speed (w/ stops) = Distance / Total Time = 60 km/hr
Distance = (90 km/hr)(t1 hr) + (0 km/hr)(t2 hr) (km)
Total Time = t1 + t2 (hr)
Solve to get
t1/t2 = 2hr/1hr
In order to Avg 60 km/hr you need 2 hrs of 90 km/hr for every 1 hour the train is stopped (0 km/hr)
OR
1/3 of every hour = 20 minutes stopped C, 40 minutes running at 90 km/hr
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