Question

A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?

• A. \(\frac{17}{4}\)
• B. \(\frac{4}{17}\)
• C. 17
• D. 390

Answer 1

The Correct Option is A

Finding the Time When the Trains Meet 

Step 1: Define Variables

• Let the time taken to meet be t hours.
• Train 1 speed = 65 km/h
• Train 2 speed = 35 km/h

Step 2: Calculate Relative Speed

\[ \text{Relative Speed} = 65 + 35 = 100 \text{ km/h} \]

Step 3: Compute Time Taken to Meet

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{390}{100} = 3.9 \text{ hours} \]

Step 4: Find the Meeting Time

The trains start at 10:00 a.m., and they take 3.9 hours to meet.

\[ 10:00 \text{ a.m.} + 3.9 \text{ hours} = 1:54 \text{ p.m.} \]

Final Answer:

The trains will meet at 1:54 p.m..