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On a 200 km track, a train travels the first 50 km at a uniform speed of 40 km/h .How fast the train must travel the next 150 km so as to maintain the average speed of 60 km/h for the whole journey?

If the train travel at 60 km/hr speed then time taken should be 20060 hour. Now it has travelled 50 km with speed 40 km/hr, so time taken is 5040 hr. So the remaining time is 20060-5040=2512 hr. The remaining distance is 200-50=150 km. So the speed is 1502512=72 km/hr. So train have to maintain average 72 km/hr speed to make total average speed of 60 km/hr.

  • 28
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let speed in the next 150 km be x km/hr
for first 50 km, speed = 40 km/hr
so time taken = 50 / 40 = 5/4 hr

for the next 150 km, speed = x
so time taken = 150/x hr

total time = 5/4 + 150/x
= (5x + 600) / 4x hr

average speed = total distance / total time
or 200 / [(5x + 600) / 4x] = 60
or (200 * 4x) / (5x + 600) = 60
or 800 x = 60 * (5x + 600)
or 800x = 300x + 36000
or 500x = 36000
or x = 36000/500 = 72 km/hr
  • 10
First let us find the time taken for the first 50 kms(t1)
t1 = distance/speed
t1 = 50/40
t1 = 5/4 hrs.

now let us find the time taken for the whole journey(T)
T = d/s
T = 200/60
T = 20/6
T = 10/3
 
now let us find the leftover time(t2)
t2 = T - t1
t2 = 10/3 - 5/4  (LCM is 12)
t2 = (40-15)/12
t2 = 25/12

now with the time and distance let us find the speed.
S = d/t
S = 150/25/12
S = 150 x 12/25( 25 x 6 =150)
S = 6 x 12
S = 72km/hr

checking
average speed = total distance/total time
Avg. Speed = 200/10/3
Avg. speed = 200 x 3/10
Avg. speed = 20 x 3
Avg. speed =  60km/hr.

Answer = 72km/hr
  • 17
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