Question

Cars A and B start at the same time, from S and T towards T and S, respectively. After passing each other at point Y, they take 6 hours 40 minutes and 3 hours 45 minutes to reach T and S, respectively. If the speed of car A is \( 60~km/h \), then how much time did Car A take to reach point Y?

• A. 4 h 15 min
• B. 5 h
• C. 3 h
• D. 5 h 30 min

Hint:

Remember the specific formula \( t = \sqrt{t_{after__meet__1} \times t_{after__meet__2}} \) for problems where objects cross and then proceed to destinations.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Two cars move towards each other, meet, and then continue to their destinations. We are given the time taken \textit{after} the meeting to reach the destinations. We need to find the time taken to meet (reach point Y). Step 2: Key Formula:
If two bodies start at the same time and meet after time \( t \), and then take \( t_1 \) and \( t_2 \) to reach their respective destinations, then: \[ t = \sqrt{t_1 \times t_2} \] Step 3: Detailed Explanation:
1. Convert times to hours: Time for Car A after meeting (\(t_1\)) = 6 hours 40 minutes = \( 6 + \frac{40}{60} = 6 + \frac{2}{3} = \frac{20}{3} \) hours. Time for Car B after meeting (\(t_2\)) = 3 hours 45 minutes = \( 3 + \frac{45}{60} = 3 + \frac{3}{4} = \frac{15}{4} \) hours. 2. Calculate meeting time (\(t\)): \[ t = \sqrt{\frac{20}{3} \times \frac{15}{4}} \] \[ t = \sqrt{\frac{300}{12}} \] \[ t = \sqrt{25} \] \[ t = 5 \text{ hours} \] Since the cars started at the same time, the time Car A took to reach point Y is exactly the meeting time \( t \). Step 4: Final Answer:
Car A took 5 hours.