If Rahul drives at a speed of 16 km/hr he reaches his destination at 6:15 pm. If he drives at speed of 20 km/hr, he reaches the same place at 5:00 pm. What time does he start and at what speed should he drive to reach same place at 12:30 am the following day?a)8 km/hr, 12:00 pmb)8 km/hr, 12:30 pmc)6 km/hr, 12:00 pmd)6 km/hr, 12:30 pmCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

To solve this problem, we need to use the concept of distance = speed × time. Let's break down the given information and solve the problem step by step.

Given Information:
- Rahul reaches his destination at 6:15 pm when driving at a speed of 16 km/hr.
- Rahul reaches the same place at 5:00 pm when driving at a speed of 20 km/hr.
- We need to find the time and speed at which Rahul should drive to reach the same place at 12:30 am the following day.

Step 1: Calculating the distance
We can calculate the distance using any of the given speeds and times. Let's use the speed of 20 km/hr and the time of 5:00 pm.
Distance = Speed × Time
Distance = 20 km/hr × 5 hours
Distance = 100 km

Step 2: Calculating the time taken at different speeds
We know that Rahul reaches his destination at 6:15 pm when driving at a speed of 16 km/hr. So, the time taken at this speed is 6:15 pm - (5:00 pm + 5 hours) = 6:15 pm - 10:00 pm = 8 hours and 15 minutes.

Step 3: Calculating the time difference
We need to find the time difference between the desired arrival time (12:30 am) and the time taken at a speed of 16 km/hr (8 hours and 15 minutes). Let's convert 12:30 am to 24-hour format, which is 00:30.
Time difference = 00:30 - (8 hours and 15 minutes)
Time difference = -7 hours and 45 minutes

Step 4: Calculating the new speed
The time difference is negative, indicating that Rahul needs to travel faster to reach the destination earlier. We can calculate the new speed using the formula:
New speed = Distance / Time difference
New speed = 100 km / (-7 hours and 45 minutes)
New speed = -100 km / (7 + 45/60) hours
New speed ≈ -100 km / 7.75 hours
New speed ≈ -12.903 km/hr

Since speed cannot be negative, we take the absolute value of the calculated speed:
New speed ≈ 12.903 km/hr

Step 5: Finding the equivalent positive speed
To find the equivalent positive speed, we round up the calculated speed to the nearest whole number. In this case, it is 13 km/hr.

Therefore, the correct answer is option A) 8 km/hr, 12:00 pm.

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