Arithmetic

Time, Speed & Distance

Medium

$A$ and $B$ are two railway stations $90 \mathrm{~km}$ apart. A train leaves $A$ at $9:00$ am, heading towards $B$ at a speed of $40 \mathrm{~km} / \mathrm{hr}$ . Another train leaves $B$ at $10:30$ am, heading towards $A$ at a speed of $20 \mathrm{~km} / \mathrm{hr}$ . The trains meet each other at

$11:45$ am

$10:45$ am

$11:00$ am

$11:20$ am

✅ Correct Option: 3

We have two trains starting from different stations at different times, moving towards each other:

Train A: Leaves station A at 9:00 am, speed = 40 km/hr

Train B: Leaves station B at 10:30 am, speed = 20 km/hr

Distance between stations: 90 km

The key insight is that Train A gets a head start of 1.5 hours before Train B even begins moving.

Since Train A leaves at 9:00 am and Train B leaves at 10:30 am:

Head start time = 10:30 am - 9:00 am = 1.5 hours

Distance covered by Train A during this head start:

$\text{Distance} = \text{Speed} \times \text{Time} = 40 \times 1.5 = 60 \text{ km}$

By the time Train B starts moving, Train A has already covered 60 km of the 90 km journey.

When Train B starts at 10:30 am:

$\text{Remaining distance} = 90 - 60 = 30 \text{ km}$

Now both trains are moving towards each other with this 30 km gap between them.

When two objects move towards each other, their relative speed is the sum of their individual speeds.

Train A speed: 40 km/hr

Train B speed: 20 km/hr

Combined speed: 40 + 20 = 60 km/hr

Time to cover the remaining 30 km:

$\text{Time} = \tfrac{\text{Distance}}{\text{Speed}} = \tfrac{30}{60} = 0.5 \text{ hours} = 30 \text{ minutes}$

The trains start moving towards each other at 10:30 am.

Meeting time = 10:30 am + 30 minutes = 11:00 am

The universal strategy for meeting problems:

Identify the head start (if any train starts earlier)

Calculate distance covered during head start

Find remaining distance when both start moving towards each other

Use relative speed (sum of individual speeds for opposite directions)

Calculate meeting time and add to the reference time

The trains meet at 11:00 am.

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