On a 100 km track, a train travels the first 30km at a uniform speed o

1.	On a 100 km track, a train travels the first 30km at a uniform speed of 30 km/h. How fastmust the train travel the next 70 km, so as toaverage 40 km/h for the entire trip?2.
Answer» Distance 1 = 30 km Distance 2 = 70 km We know that speed = distance/time and, Average speed = total distance/total time taken When the train acquired a speed of 30 km/hr, the time taken = 30/30 = 1 hour Average speed = 9distance 1 + distance 2)/(time 1 + time 2) AS time 2 or t2 is time taken for the second part of the journey of 70 km ⇒ 40 = 100/(1 + t2) ⇒ 40 + 40t2 = 100 ⇒ 40t2 = 100 - 40 ⇒ 40t2 = 60 ⇒ t2 = 60/40 ⇒ t2 = 1.5 So, t2 or time taken to travel the second part of the journey is 1.5 hours. Speed of the second part of the journey = distance 2/time 2 ⇒ 70/1.5 ⇒ 46.666 km/hr or 46.7 km/hr

On a 100 km track, a train travels the first 30km at a uniform speed of 30 km/h. How fastmust the train travel the next 70 km, so as toaverage 40 km/h for the entire trip?2.

Answer»

Distance 1 = 30 km

Distance 2 = 70 km

We know that speed = distance/time

and, Average speed = total distance/total time taken

When the train acquired a speed of 30 km/hr, the time taken = 30/30 = 1 hour

Average speed = 9distance 1 + distance 2)/(time 1 + time 2)

AS time 2 or t2 is time taken for the second part of the journey of 70 km

⇒ 40 = 100/(1 + t2)

⇒ 40 + 40t2 = 100

⇒ 40t2 = 100 - 40

⇒ 40t2 = 60

⇒ t2 = 60/40

⇒ t2 = 1.5

So, t2 or time taken to travel the second part of the journey is 1.5 hours.

Speed of the second part of the journey = distance 2/time 2

⇒ 70/1.5

⇒ 46.666 km/hr or 46.7 km/hr

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