A train starts from station A at 9 A.M. travels at 50 km / hr towards station B, 210 km away.

step 1 Hi, here in this given problem, there are the two stations, P and Q. The gap between them means

A train starts from station A at 9 A.M. travels at 50 km /...

A train starts from station $A$ at 9 A.M. travels at $50 \mathrm{~km} / \mathrm{hr}$ towards station $B, 210 \mathrm{~km}$ away. Another train starts from station $B$ at 11 A.M. and travels at $60 \mathrm{~km} / \mathrm{hr}$ towards station $A$. At what distance from $A$, will they meet? (a) $150 \mathrm{~km}$ (b) $200 \mathrm{~km}$ (c) $250 \mathrm{~km}$ (d) None of these

A train starts from station $A$ at 9 A.M. travels at $50 \mathrm{~km} / \mathrm{hr}$ towards station $B, 210 \mathrm{~km}$ away. Another train starts from station $B$ at 11 A.M. and travels at $60 \mathrm{~km} / \mathrm{hr}$ towards station $A$. At what distance from $A$, will they meet?
(a) $150 \mathrm{~km}$
(b) $200 \mathrm{~km}$
(c) $250 \mathrm{~km}$
(d) None of these

Key Concepts

Distance-Speed-Time Relationship

This fundamental concept connects distance, speed, and time through the formula d = v × t. It is essential for calculating how far an object travels given its constant speed over a specific period, which forms the basis of many kinematics problems.

Relative Speed

Relative speed is used when two objects are moving towards or away from each other and is calculated by combining their speeds appropriately. In meeting point problems, it allows for the simplification of the system by treating the motion as if one object were stationary while the other moves at the combined speed, making it easier to determine the time and location of their encounter.

Head Start Calculation

In motion problems where one object begins its journey before the other, the distance covered during this initial time difference, or head start, must be accounted for. This concept is key in adjusting the calculations to accurately determine how the positions of the objects evolve before they start interacting.

Uniform Motion and Meeting Point Problems

These problems involve objects moving at constant speeds along a straight line, and the goal is to find when and where they meet. Setting up equations based on the distance-speed-time relationships of both objects and accounting for factors like head starts and relative speed allows for the determination of the meeting point.

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