Question

A boy travels with speeds 10km/hr,20km/hr,30km/hr for 3 successive journey distances are in the ratio 2:1:3.Find the average speed of the boy​

Answer 1

The average speed is 300/19 kmph or 15.789 kmph

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Answer 2

Answer :

Average speed of the boy​ $= 17.14km/hr$

Explanation:

• Average speed $= \frac{Total - distance}{Total-Time }$

Let the distances covered in successive journey be  $2x,1x,3x.$

we know that,

$Speed = \frac{distance }{time}$

$Time = \frac{Distance}{Speed}$

Let $t_{1} ,t_{2} ,t_{3}$ be the time taken by boy during successive journey.

• $2x$ be the distance travelled by boy with speed $10km/hr$.

                        $t_{1} =\frac{2x}{10}$

• $1x$ be the distance travelled by boy with speed $20km/hr$.

                      $t_{2} = \frac{1x}{20}$

• $3x$ be the distance travelled by boy with speed $30km/hr$.

                       $t_{3} = \frac{3x}{30}$

                   Average speed of a boy $= \frac{Total - distance}{Total-Time }$

                                                             $= \frac{ 1x+2x+3x}{t_{1} + t_{2} + t_{3} }$

                                                          $= \frac{6x}{\frac{2x}{10}+ \frac{1x}{20} +\frac{3x}{30}}$

                                                           $= \frac{6}{\frac{2}{10}+ \frac{1}{20} +\frac{3}{30}}$

                                                         $= \frac{6}{\frac{2}{10}+ \frac{1}{20} +\frac{1}{10}}$

                                                             $= \frac{6}{\frac{3}{10}+ \frac{1}{20} }$

                                                         $= \frac{6}{\frac{6}{20}+ \frac{1}{20} }$

                                                       $= \frac{6}{\frac{7}{20} }$

                                                      $= \frac{6*20}{7}$

                                                     $= \frac{120}{7}$

                                                  $= 17.14km/hr$

Therefore, average speed of the boy​ $= 17.14km/hr$

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