Mohan walks from Tilak Nagar to Moti Nagar and back in a...

Mohan walks from Tilak Nagar to Moti Nagar and back in a certain time at the rate of $3 \frac{1}{2} \mathrm{~km} / \mathrm{hr}$ But if he had walked from Tilak Nagar to Moti Nager at the rate of $3 \mathrm{~km} / \mathrm{hr}$ and back from Moti Nagar to Tilak Nagar at the rate of $4 \mathrm{~km} / \mathrm{hr}$., he would have taken 10 minutes longer. The distance between Tilak Nagar and Moti Nagar is (a) $28 \mathrm{~km}$ (b) $32 \mathrm{~km}$ (c) $24 \mathrm{~km}$ (d) None of these

Mohan walks from Tilak Nagar to Moti Nagar and back in a certain time at the rate of $3 \frac{1}{2} \mathrm{~km} / \mathrm{hr}$ But if he had walked from Tilak Nagar to Moti Nager at the rate of $3 \mathrm{~km} / \mathrm{hr}$ and back from Moti Nagar to Tilak Nagar at the rate of $4 \mathrm{~km} / \mathrm{hr}$., he would have taken 10 minutes longer. The distance between Tilak Nagar and Moti Nagar is
(a) $28 \mathrm{~km}$
(b) $32 \mathrm{~km}$
(c) $24 \mathrm{~km}$
(d) None of these

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Key Concepts

Algebraic Equation Setup

When different scenarios or conditions are provided, such as variations in speed along different parts of a journey, establishing algebraic equations becomes necessary. This process involves expressing the time or distance in terms of variables and then equating expressions based on consistent total times or distances to solve for the unknown quantity.

Understanding of Round Trip with Variable Speeds

In problems where a journey is made with different speeds in each direction, setting up the relation for the total time of the round trip using individual segment times is crucial. This helps in comparing scenarios with constant and variable speeds, leading to equations that reveal the underlying relationships among distance, speed, and time.

Distance-Speed-Time Relationship

This concept involves the fundamental formula, distance = speed × time, which is essential for understanding how far an object moves given its speed and the duration of its motion. It allows one to calculate any one of the three variables if the other two are known, forming the basis for solving uniform motion problems.

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