Mr. Kumar drives to work at an average speed of 48 Km/hr. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?
This problem can be solved by treating the given "average speed" as the constant speed for the entire journey. The information about the time difference between the two parts of the trip allows us to find the total distance.
1. Define Variables and Convert Units - Let the total distance to the office be D km.
- The speed is constant at 48 km/hr.
- The given time difference is 10 minutes, which is 10/60 = 1/6 of an hour.
2. Set Up an Equation Using the Time Difference - We use the formula: Time = Distance / Speed.
- Time for the first 60% of the journey (a distance of 0.6D) is t1 = (0.6D) / 48.
- Time for the remaining 40% of the journey (a distance of 0.4D) is t2 = (0.4D) / 48.
- The problem states that t1 is 1/6 hour more than t2, so: (t1 - t2) = 1/6.
3. Solve for the Total Distance (D) - (0.6D / 48) - (0.4D / 48) = 1/6
- (0.6D - 0.4D) / 48 = 1/6
- 0.2D / 48 = 1/6
- 0.2D = 48 / 6
- 0.2D = 8
- D = 8 / 0.2 = 40 km.
Final Answer: The office is 40 Kms far.
Reinforce your conceptual grasp with related questions from NIMCET 2020:
Which of the four options should fill the missing cell?
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