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
• E.

Hint:

When two objects move towards each other, their relative speed is the sum of their individual speeds. Use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}. \]

Answer 1

The Correct Option is A

Step 1: Define the time variable. Let the time taken for the two trains to meet be \( t \) hours. - Train 1 travels at a speed of 65 km/h. - Train 2 travels at a speed of 35 km/h. Since the trains are moving towards each other, their relative speed is: \[ 65 + 35 = 100 \text{ km/h}. \] Step 2: Calculate the time to meet. The total distance between them is 390 km. Using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{390}{100} = 3.9 \text{ hours}. \] Step 3: Determine the meeting time. The trains start at 10:00 a.m., so adding 3.9 hours: \[ 10:00 \, \text{a.m.} + 3 \, \text{hours and} \, 54 \, \text{minutes} = 1:54 \, \text{p.m.} \] Thus, the trains will meet at 1:54 p.m.