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A man goes from C to D at 40 km/h and he returns from D to C at x km/h. If the average speed of the man for the whole journey is 60 km/h, then what is the value of x? (SSC MTS 2018)
- a)100
- b)120
- c)110
- d)80
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A man goes from C to D at 40 km/h and he returns from D to C at x km/h...
We have given the average speed of the man = 60 km/h
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A man goes from C to D at 40 km/h and he returns from D to C at x km/h...
Understanding the Problem
A man travels from point C to D at a speed of 40 km/h and returns from D to C at a speed of x km/h. We need to find the value of x given that the average speed for the entire journey is 60 km/h.
Concept of Average Speed
The average speed for a round trip is calculated as:
Average Speed = Total Distance / Total Time
Calculating Total Distance
Let the distance from C to D be d km. The total distance for the round trip (C to D and back to C) is:
Total Distance = d + d = 2d km
Calculating Total Time
- Time taken to travel from C to D = Distance / Speed = d / 40 hours
- Time taken to return from D to C = d / x hours
Thus, the total time taken for the journey is:
Total Time = (d / 40) + (d / x) hours
Setting Up the Equation
According to the average speed formula:
60 = Total Distance / Total Time
Substituting the values:
60 = 2d / [(d / 40) + (d / x)]
Simplifying the Equation
Multiplying both sides by the total time:
60[(d / 40) + (d / x)] = 2d
This simplifies to:
(60d / 40) + (60d / x) = 2d
Which reduces to:
(3d / 2) + (60d / x) = 2d
Solving for x
Now, isolating the terms gives:
60d / x = 2d - (3d / 2)
This simplifies to:
60d / x = (4d - 3d) / 2
Resulting in:
60 / x = 1 / 2
Now, solving for x:
x = 120 km/h
Conclusion
Thus, the value of x is 120 km/h, which confirms that the answer is option 'B'.
A man travels from point C to D at a speed of 40 km/h and returns from D to C at a speed of x km/h. We need to find the value of x given that the average speed for the entire journey is 60 km/h.
Concept of Average Speed
The average speed for a round trip is calculated as:
Average Speed = Total Distance / Total Time
Calculating Total Distance
Let the distance from C to D be d km. The total distance for the round trip (C to D and back to C) is:
Total Distance = d + d = 2d km
Calculating Total Time
- Time taken to travel from C to D = Distance / Speed = d / 40 hours
- Time taken to return from D to C = d / x hours
Thus, the total time taken for the journey is:
Total Time = (d / 40) + (d / x) hours
Setting Up the Equation
According to the average speed formula:
60 = Total Distance / Total Time
Substituting the values:
60 = 2d / [(d / 40) + (d / x)]
Simplifying the Equation
Multiplying both sides by the total time:
60[(d / 40) + (d / x)] = 2d
This simplifies to:
(60d / 40) + (60d / x) = 2d
Which reduces to:
(3d / 2) + (60d / x) = 2d
Solving for x
Now, isolating the terms gives:
60d / x = 2d - (3d / 2)
This simplifies to:
60d / x = (4d - 3d) / 2
Resulting in:
60 / x = 1 / 2
Now, solving for x:
x = 120 km/h
Conclusion
Thus, the value of x is 120 km/h, which confirms that the answer is option 'B'.
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