A train traveled a certain route that consisted of 3 segments.

Question

A train traveled a certain route that consisted of 3 segments. The second segment lasted twice as long as the first one and the third segment lasted twice as long as the second one. If the average speeds of the train in these segments were 60 km/h, 75 km/h, 35 km/h, what was the average speed of the train, in km/h, over the entire route?

A. 40
B. 50
C. 60
D. 70
E. 80

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Bunuel · Accepted Answer

Official Solution:

A train traveled a certain route that consisted of 3 segments. The second segment lasted twice as long as the first one and the third segment lasted twice as long as the second one. If the average speeds of the train in these segments were 60 km/h, 75 km/h, 35 km/h, what was the average speed of the train, in km/h, over the entire route?

A. 40
B. 50
C. 60
D. 70
E. 80

Let's assume the time spent on the first segment was  t  hours,  2t  hours on the second, and  4t  hours on the third. The entire journey lasted  t + 2t + 4t = 7t  hours. The distances for the segments are  60t  km,  75 * 2t = 150t  km, and  35 * 4t = 140t  km, respectively. Thus, the average speed over the entire route would be  \frac{	ext{total distance}}{	ext{total time}} = \frac{60t + 150t + 140t}{7t} = 50  km/h.

Answer: B

a191291r · Answer

To find the average speed of the train over the entire route, we need to first determine the total distance and the total time taken for the journey. The average speed is given by:

Average Speed = \frac{Total Distance}{Total Time}

Let's denote:
- "t" as the time for the first segment,

We are given that:
time for the second segment = 2*t = 2t
time for the third segment = 2*2t = 4t
Therefore, the total time  T = t+2t+4t = 7t

Now, let the distances for the three segments be a, b, c respectively

We have,
 a = 60 * t = 60t 
 b = 75 * 2t = 150t 
 c = 35 * 4t = 140t

Next, we calculate the total distance D

D=a+b+c 
 D=60t+150t+140t=350t

Finally, we find the average speed  V = \frac{Total Distance}{Total Time} = \frac{D}{T} = \frac{350t}{7t} = 50km/h

Answer: B

Scholar94 · Answer

Answer B:

Though a typical work-rate question, we can look at is as a Weighted average problem.

Let x T1 T2 and T3 be the time spent for each of the 3 routs

T1=x, 
T2=2x
T3=4x

Average speed= (T1×S1+T2×S2+T3×S3)/T1+T2+T3

Where s1,s2 and s3 are the speeds for each of the root

/7x=350x/7x=50

Posted from my mobile device

HarishD · Answer

Answer B: Please refer the below image for explanation

Tushar2804 · Answer

Average speed through a journey will be the total distance per total time.

I went with the assumption here that the first part of the journey was 1 hour. Which means, from the data given, 2nd part was 2 hours and the 3rd part was 4 hours. 
Distance wise, for each part it will be the product of speed in that part with the time they took. 
So total distance = 60 + (75*2) + (35*4) = 350 kms. 
Total Time = 1 + 2 + 4 = 7 hours.

So, average speed = 350/7 = 50 kmph.

btsaami · Answer

1. Here I can use balancing:
 In the first segment, 60 in the next two 75 can be written as 75 75 in each of the next two sub segments and so on.
Therefore we get below series:
60 75 75 35 35 35 35

Now from the option we can see that majority is 35 therefore average speed can't be D and E. And also c. But may be check once for B and C.

Find the distance from the mean, it should be equal to 0. 
With option c, we get the following:
60-60, 75-60, 75-60, 4 times 35-60
0,15,15,-25,-25,-25,-25
Not adding to zero.
If we repeat the same thing for B we get.
10+25+25-15*4=0
Hence b is the correct option.

2. Segregate the speeds as below
60 75 75 35 35 35 35

Find the average
350/7= 50

Posted from my mobile device

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A train traveled a certain route that consisted of 3 segments.

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A train traveled a certain route that consisted of 3 segments.