Question

4. A car is moving on a straight road covers one third of the distance with a speed of 20 km/h and the rest with
a speed of 60 km/h. The average speed of the car is
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Answer 1

GIVEN :-

• Speed for  one third of distance , $\sf V_1$ = 20 km/h

• Speed for two third of distance , $\sf V_2$ = 60 km/h

TO FIND :-

• Average speed of the car

SOLUTION :-

    Let the total distance be 3x .

   

    Time take to cover one third of distance , $\sf t_1 = \dfrac{x}{20}$

    Time taken to cover two third of distance , $\sf t_2 = \dfrac{2x}{60}=\dfrac{x}{30}$

      $\bf Average \ speed = \dfrac{Total \ Distance }{Total \ Time }$

       $\hookrightarrow \sf Average \ speed = \dfrac{3x}{\dfrac{x}{20}+\dfrac{x}{30}}$

                                  $= \sf \dfrac{3x}{\dfrac{30x+20x}{20\times 30}}$

                                  $=\sf \dfrac{3x}{\dfrac{50x}{600}}$

                                  $\sf = \dfrac{3x}{\dfrac{x}{12}}$

                                  $=\sf 3x \times \dfrac{12}{x}$

                                  $=\sf 3\times 12$

                                  $\bf = 36 \ km/h$