Question

A car covers first half of the distance between two places at a speed of 80km/hr and the second half at 60km/hr. what is the average speed​

Answer 1

Given

A car covers first half of the distance between two places at a speed of 80 km/hr and the second half at 60 km/hr

To Find

Average Speed

Formula Applied

Average speed is given by ,

$\bf \pink{\bigstar\ \; V_{avg}=\dfrac{2V_1V_2}{V_1+V_2}}$

where ,

• V₁ denotes speed 1
• V₂ denotes speed 2

Average speed is given by ,

$\bf \blue{V_{avg}=\dfrac{T_{Ditance}}{T_{time}}}$

where ,

• T denotes Total

Solution

Method - 1 :

Speed 1 = 80 km/h

Speed 2 = 60 km/h

Apply formula for average speed ,

$\bf \green{V_{avg}=\dfrac{2(80)(60)}{80+60}}\\\\\to \rm V_{avg}=\dfrac{2(80)(60)}{140}\\\\\leadsto \bf \blue{V_{avg}=68.57\ km/h\ \; \bigstar}$

Method - 2 :

Let total distance b/w two places be " x "

Apply formula for Average Speed ,

$\bf V_{Avg}=\dfrac{T_{Distance}}{T_{Time}}\\\\\to \rm V_{Avg}=\dfrac{x}{t_1+t_2}\\\\\to \rm V_{Avg}=\dfrac{x}{\frac{x/2}{80}+\frac{x/2}{60}}$

From ,  $\bf Time=\dfrac{Distance}{Speed}$

$\to \rm V_{Avg}=\dfrac{x}{\frac{x}{160}+\frac{x}{120}}\\\\\to \rm V_{Avg}=\dfrac{x}{\frac{30x+40x}{4800}}\\\\\to \rm V_{Avg}=\dfrac{4800x}{70x}\\\\\leadsto \bf \red{V_{Avg}=68.57\ km/h\ \; \bigstar}$

Answer 2

Answer:

Let the Total Distance be D

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Speed_{Avg}=\dfrac{Total\:Distance}{Total \: Time}\\\\\\:\implies\sf Speed_{Avg}=\dfrac{D}{t_1+t_2}\\\\\\:\implies\sf Speed_{Avg}=\dfrac{D}{\frac{D}{2 \times 80}+\frac{D}{2 \times 60}}\\\\\\:\implies\sf Speed_{Avg}=\dfrac{D}{\frac{D}{160}+\frac{D}{120}}\\\\\\:\implies\sf Speed_{Avg}=\dfrac{x}{\frac{30x+40x}{4800}}\\\\\\:\implies\sf Speed_{Avg}=\dfrac{4800x}{70x}\\\\\\:\implies\underline{\boxed{\sf Speed_{Avg}=68.57\: km/h}}$

⠀

$\therefore\:\underline{\textsf{Average Speed of car is \textbf{68.57 km/h}}}.$