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With average speed of 40km/hour, a train reaches its destination in time. If it goes with an average speed of 35 km hour, it is late by 15 minutes. The total journey is
- a)30 km
- b)40 km
- c)70 km
- d)80 km
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
With average speed of 40km/hour, a train reaches its destination in ti...
Understanding the Problem
To solve the problem, we need to analyze the information given about the train's journey at two different speeds.
Key Information
- Average speed of the train at first scenario: 40 km/h
- Average speed of the train at second scenario: 35 km/h
- Delay when traveling at 35 km/h: 15 minutes (which is 0.25 hours)
Setting Up the Equation
Let the distance of the journey be 'D' km.
Time Calculation at 40 km/h
- Time taken to reach the destination on time:
Time = Distance / Speed
Time = D / 40 hours
Time Calculation at 35 km/h
- Time taken when late:
Time = D / 35 hours
Late Time Relationship
According to the problem, when the train goes at 35 km/h, it is late by 15 minutes (0.25 hours). Therefore, we can set up the equation:
(D / 35) - (D / 40) = 0.25
Finding a Common Denominator
The least common multiple of 35 and 40 is 280. Rewriting the equation:
- D/35 = 8D/280
- D/40 = 7D/280
Now substituting back into the equation:
(8D/280) - (7D/280) = 0.25
This simplifies to:
D/280 = 0.25
Solving for D
Multiplying both sides by 280 gives:
D = 0.25 * 280
D = 70 km
Conclusion
Thus, the total journey distance is 70 km, which corresponds to option 'C'.
To solve the problem, we need to analyze the information given about the train's journey at two different speeds.
Key Information
- Average speed of the train at first scenario: 40 km/h
- Average speed of the train at second scenario: 35 km/h
- Delay when traveling at 35 km/h: 15 minutes (which is 0.25 hours)
Setting Up the Equation
Let the distance of the journey be 'D' km.
Time Calculation at 40 km/h
- Time taken to reach the destination on time:
Time = Distance / Speed
Time = D / 40 hours
Time Calculation at 35 km/h
- Time taken when late:
Time = D / 35 hours
Late Time Relationship
According to the problem, when the train goes at 35 km/h, it is late by 15 minutes (0.25 hours). Therefore, we can set up the equation:
(D / 35) - (D / 40) = 0.25
Finding a Common Denominator
The least common multiple of 35 and 40 is 280. Rewriting the equation:
- D/35 = 8D/280
- D/40 = 7D/280
Now substituting back into the equation:
(8D/280) - (7D/280) = 0.25
This simplifies to:
D/280 = 0.25
Solving for D
Multiplying both sides by 280 gives:
D = 0.25 * 280
D = 70 km
Conclusion
Thus, the total journey distance is 70 km, which corresponds to option 'C'.
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