Mr. Prasad travelled equal distances at speeds of 2 km / hr, 4 km / hr, and 6 km / hr, and to

Step 1: Let the distance travelled at each speed be ( d ) km. Since Mr. Prasad travelled equal d

Mr. Prasad travelled equal distances at speeds of 2 km /...

Mr. Prasad travelled equal distances at speeds of $2 \mathrm{~km} / \mathrm{hr}, 4 \mathrm{~km} / \mathrm{hr}$, and $6 \mathrm{~km} / \mathrm{hr}$, and took a total of 55 minutes to complete. Find the total distance he travelled, in $\mathrm{km}$.
(a) 2
(b) 1
(c) 4
(d) 3

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Key Concepts

Distance-Rate-Time Relationship

This concept involves the fundamental equation d = rt, where d represents distance, r represents speed (rate), and t represents time. It is central in solving problems that involve finding one of these variables when the other two are known, and it allows one to analyze each segment of a journey separately before combining them to form an overall understanding.

Unit Conversion

In many real-world problems, it is necessary to convert units so that all measurements are compatible. For example, time may be given in minutes while speed is provided in kilometers per hour. Converting minutes to hours makes it possible to directly apply the distance-rate-time formula.

Aggregating Time over Multiple Segments

When a journey is divided into different segments going at varying speeds, the total time spent is the sum of the times for each individual segment. This aggregated time is then equated with the total journey duration to solve for unknowns such as the distance covered in each segment.

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