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The distance between two stations A and B is 778 km. A train covers th 10 Dec 2020, 10:45
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D
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35% (medium)

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74% (02:36) correct 26% (03:10) wrong based on 165 sessions

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The distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey.

A. 30.3 km/hr

B. 35.0 km/hr

C. 57.5 km/hr

D. 67.2 km/hr

E. 68.2 km/hr
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D
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The distance between two stations A and B is 778 km. A train covers th 10 Dec 2020, 11:07
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Average speed = Total distance / Total time taken

Time is taken from A to B = 778/84 = 09.25
Time is taken from B to A = 778/56 = 13.90

Average Speed = 778*2 / (9.25+13.90)
Average Speed = 1556 / 23.15
Average Speed = 67.2

Answer is D
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The distance between two stations A and B is 778 km. A train covers th 10 Dec 2020, 11:11
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Given: The distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour.
Asked: Find the average speed of train during the whole journey.

Total distance = 778*2 = 1556 km
Total time = 778/84 + 778/56 = 23.15 hours
Average speed = 1556/23.15 = 67.2 km/hr

IMO D
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The distance between two stations A and B is 778 km. A train covers th 04 May 2022, 07:29
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The whole journey here represents a round-trip, since the train started from A and eventually came back to A.

In a round trip, the average speed is given by the formula,

Average Speed = \(\frac{2 a b }{ (a +b)}\), where

a = Speed of the object during the onward journey
b = Speed of the object during the return journey

The data about the distance between the two cities, is not needed, if we follow this approach to answer the question.

In this question, a = 84 and b = 56.
Substituting these values into the standard expression, we have,

Average speed = \(\frac{2 * 84 * 56 }{ (84 + 56)}\) =\(\frac{ 2 * 84 * 56 }{ (140)}\).

Simplifying, we have, Average speed = \(\frac{336 }{ 5}\).

67 * 5 = 335 and 68 * 5 = 340. Therefore, the value of \(\frac{336 }{ 5}\) has to be in between 67 and 68 which means the only value possible is 67.2

The correct answer option is D.
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The distance between two stations A and B is 778 km. A train covers th 29 Nov 2024, 00:43
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