Question

A man walks half of journey 4 km/hr by cycle does 1/3 of journey at 12 km/hr and rides the remainder journey in 9 km hr

Answer 1

Please see the attachment

Answer 2

Answer:

Average speed = 5.84 km/h

Step-by-step explanation:

Let the total distance covered by a man be x km

Case 1: Speed = 4 km/h and distance, $d_1=\dfrac{x}{2}$

            $t_1=\dfrac{x}{8}$

Case 2: Speed = 12 km/h and distance, $d_2=\dfrac{x}{3}$

            $t_2=\dfrac{x}{36}$

Case 3: Speed = 9 km/h and distance, $d_3=x-\dfrac{x}{2}-\dfrac{x}{3}=\dfrac{x}{6}$

            $t_3=\dfrac{x}{54}$

$\text{Average Speed}=\dfrac{\text{Total distance}}{\text{Total time}}$

$\text{Average Speed}=\dfrac{d_1+d_2+d_3}{t_1+t_2+t_3}$

$\text{Average Speed}=\dfrac{\dfrac{x}{2}+\dfrac{x}{3}+\dfrac{x}{6}}{\dfrac{x}{8}+\dfrac{x}{36}+\dfrac{x}{54}}$

$\text{Average Speed}=\dfrac{x}{\dfrac{37x}{216}}$

$\text{Average Speed}=\dfrac{216}{37}$

$\text{Average Speed}\approx 5.84 \text{ km/h}$