Two stations A and B are 100 km apart on a straight line. One train starts from A at 7 A.M. and

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Two stations A and B are 100 km apart on a straight line....

Two stations $A$ and $B$ are $100 \mathrm{~km}$ apart on a straight line. One train starts from $A$ at 7 A.M. and travels towards $B$ at $20 \mathrm{~km} / \mathrm{hr}$ speed. Another train starts from $B$ at 8 A.M. and travels towards $A$ at $25 \mathrm{~km} / \mathrm{hr}$ speed. At what time will they meet? (a) 10.30 A.M. (b) 11 A.M. (c) 10 A.M. (d) None of these

Two stations $A$ and $B$ are $100 \mathrm{~km}$ apart on a straight line. One train starts from $A$ at 7 A.M. and travels towards $B$ at $20 \mathrm{~km} / \mathrm{hr}$ speed. Another train starts from $B$ at 8 A.M. and travels towards $A$ at $25 \mathrm{~km} / \mathrm{hr}$ speed. At what time will they meet?
(a) 10.30 A.M.
(b) 11 A.M.
(c) 10 A.M.
(d) None of these

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Key Concepts

Time-Distance Relationship

The time-distance relationship is a core concept in kinematics, emphasizing that travel time is directly related to the distance covered and inversely related to the speed of movement. This relationship is used to set up equations that can be solved to determine unknown variables such as the meeting time of two moving objects.

Staggered Start Times

Staggered start times refer to scenarios where moving objects begin their journeys at different times. To analyze such problems, the time difference must be taken into account, often resulting in an initial head start for one of the objects. Adjusting for this head start is crucial to accurately calculating when the two objects will meet.

Uniform Motion

Uniform motion refers to movement at a constant speed in a straight line. In such scenarios, the distance traveled is directly proportional to the time elapsed, following the formula distance = speed × time, which is fundamental in solving problems involving constant speeds.

Relative Speed

Relative speed is the effective speed at which the gap between two moving objects closes when they are traveling towards each other. It is found by adding the speeds of the two objects if they are moving in opposite directions, which simplifies the process of determining meeting times.

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