Question

A train leaves Station A at 6:00 AM and travels towards Station B at a constant speed of 60 km/h. Another train leaves Station B at 8:00 AM and travels towards Station A at a constant speed of 90 km/h. The distance between the two stations is 540 km. At what time will the two trains meet?

• A. 9:48 AM
• B. 10:48 AM
• C. 11:45 AM
• D. 12:45 AM

Answer 1

Answer:

B. 10:48 AM

Let the trains meet (t) hours after 6:00 AM.

Step 1: Distance covered by the first train

The first train starts at 6:00 AM and travels at 60 km/h.

$\text{Distance covered by Train A} = 60t$

Step 2: Distance covered by the second train

The second train starts at 8:00 AM, which is 2 hours later.

So by the meeting time, it has traveled ((t-2)) hours at 90 km/h.

$\text{Distance covered by Train B} = 90(t-2)$

Step 3: Total distance is 540 km

$60t + 90(t-2) = 540$
$60t + 90t - 180 = 540$
$150t = 720$
$t = \frac{720}{150} = 4.8 \text{ hours}$

Step 4: Convert 4.8 hours to hours and minutes

$0.8 \times 60 = 48 \text{ minutes}$

So the trains meet 4 hours 48 minutes after 6:00 AM.

$6:00\ \text{AM} + 4\ \text{hours}\ 48\ \text{minutes}$
$= 10:48\ \text{AM}$