A man walks 6 km at a speed of 1 (1)/(2) km / hr, runs 8 km at a speed of 2 km / hr and goes

step 1 Now a question is a man walks on a straight road from his home to a market 2 .5 km away with a s

A man walks 6 km at a speed of 1 (1)/(2) km / hr, runs 8...

A man walks $6 \mathrm{~km}$ at a speed of $1 \frac{1}{2} \mathrm{~km} / \mathrm{hr}$, runs $8 \mathrm{~km}$ at a speed of $2 \mathrm{~km} / \mathrm{hr}$ and goes by bus another $32 \mathrm{~km}$. Speed of the bus is $8 \mathrm{~km} / \mathrm{hr}$. If the speed of the bus is considered as the speed of the man, find the average speed of the man. (a) $4 \frac{5}{6} \mathrm{~km} / \mathrm{hr}$ (b) $3 \frac{5}{6} \mathrm{~km} / \mathrm{hr}$ (c) $5 \frac{7}{6} \mathrm{~km} / \mathrm{hr}$ (d) None of these

A man walks $6 \mathrm{~km}$ at a speed of $1 \frac{1}{2} \mathrm{~km} / \mathrm{hr}$, runs $8 \mathrm{~km}$ at a speed of $2 \mathrm{~km} / \mathrm{hr}$ and goes by bus another $32 \mathrm{~km}$. Speed of the bus is $8 \mathrm{~km} / \mathrm{hr}$. If the speed of the bus is considered as the speed of the man, find the average speed of the man.
(a) $4 \frac{5}{6} \mathrm{~km} / \mathrm{hr}$
(b) $3 \frac{5}{6} \mathrm{~km} / \mathrm{hr}$
(c) $5 \frac{7}{6} \mathrm{~km} / \mathrm{hr}$
(d) None of these

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Key Concepts

Time Calculation from Distance and Speed

This concept involves determining the time taken to cover a certain distance when traveling at a specific speed. The relationship is given by the formula time = distance ÷ speed, which is critical for analyzing trips that comprise multiple segments with varying speeds.

Segmented Motion Analysis

When a journey is divided into different segments where each segment is traveled at a different speed, the overall motion must be analyzed by calculating the time taken for each segment individually. The sum of these times, in conjunction with the total distance, allows for the determination of the average speed. This method is fundamental in solving problems involving varied velocities.

Average Speed

Average speed is a measure of the overall rate at which distance is covered during a journey. It’s calculated by dividing the total distance traveled by the total time taken. This concept is essential in understanding how variations in speed over different segments of a trip can affect the overall pace of motion.

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