Question

arjun complete distance of 1000 km in 4 hours between pune to goa. he returned at the speed of 3 km/hr.
avg. speed of yatra?​

Answer 1

Correct Question :

Arjun Complete travels a distance of 1000 km with speed 4 km/hr and returns with speed of 3 km/hr. Find Average Speed of Total Journey.

AnswEr :

• Time Taken with Speed 4 km/hr :

$\longrightarrow\tt Distance = Speed \times Time\\\\\\\longrightarrow\tt 1000 = 4 \times Time\\\\\\\longrightarrow\tt Time = \dfrac{1000}{4}\\\\\\\longrightarrow\tt Time = 250$

• Time Taken with Speed 3 km/hr :

$\longrightarrow\tt Distance = Speed \times Time\\\\\\\longrightarrow\tt 1000 = 3 \times Time\\\\\\\longrightarrow\tt Time = \dfrac{1000}{3}$

$\rule{200}{1}$

• A V E R A G E ⠀S P E E D :

$:\implies\tt Average\:Speed = \dfrac{Total\: Distance}{Total\:Time}\\\\\\:\implies\tt Average\:Speed = \dfrac{1000+1000}{250+\dfrac{1000}{3}}\\\\\\:\implies\tt Average\:Speed = \dfrac{2000}{ \dfrac{750 + 1000}{3} }\\\\\\:\implies\tt Average\:Speed = \dfrac{2000 \times 3}{1750}\\\\\\:\implies\tt Average\:Speed = \frac{6000}{1750}\\\\\\:\implies \boxed{\tt Average\:Speed = 3.43 \:km/hr}$

⠀

$\therefore\:\underline{\textsf{Average Speed of Total Journey is \textbf{3.43 Km/hr}}}$

$\rule{200}{2}$

• S H O R T C U T ⠀T R I C K :

When Distance of Journey from Both side is Same then, Average Speed is :

$:\implies\sf Average\: Speed = \dfrac{2 \times Speed_1 \times Speed_2}{Speed_1 + Speed_2}\\\\\\:\implies\sf Average\: Speed =\dfrac{2 \times 4 \times 3}{4 + 3} \\\\\\:\implies\sf Average\: Speed =\dfrac{24}{7} \\\\\\:\implies \boxed{\sf Average\: Speed =3.43 \:km/hr}$

⠀

$\therefore\:\underline{\textsf{Average Speed of Total Journey is \textbf{3.43 Km/hr}}}$

Answer 2

Answer:

${\boxed{\bold\red{Average\:speed=b)3.43\:km/h }}}$

Step-by-step explanation:

Correct question:-

Arjun completes a distance of 1000 km in 4 hours between pune to goa. He returned at a speed of 3 km/h.Average speed of Arjun?

We know that,

$\bullet$ ${\boxed{\bold\green{Speed=\dfrac{Distance}{Time} }}}$

$\bullet {\boxed{\bold\green{Average\:speed=\dfrac{Total\:distance}{Total\:time} }}}$

$\rule{300}{1}$

$\tt Total\:distance = (1000+1000)\:km$

→ $\tt Total\:distance = 2000 \:km$

$\rule{300}{1}$

$\tt Total\:time = Time\:at\:4\:km/h + Time\:at\:3\:km)h$

↓ $\tt Total\:time = \dfrac{Distance_1}{Speed_1} +\dfrac{Distance_1}{Speed_2}$

→ $\tt Total\:time =\dfrac{1000}{4} + \dfrac{1000}{3}$

→ $\tt Total\:time = (250 + 333.33)\:h$

→ $\tt Total\:time = 583.33\:h$

$\rule{300}{1}$

$\tt Average\:speed = \dfrac{Total\:distance}{Total\:time}$

→ $\tt Average\:speed =\dfrac{2000\:km}{583.33\:h}$

→ ${\boxed{\tt\red{Average\:speed = 3.43\:km/h}}}$

$\therefore\bold{\underline{Average\:speed\:of\:Arjun=3.43\:km/h}}$