Question

abdul,while driving to school ,computes the speed for his trip to be 20 kmh-1 .on his return trip along the same route there is less traffic and speed is 30kmh-1.what is the average speed for abdul's overall trip?

Answer 1

GIVEN:-

• Initial Speed of trip = 20km/h

• Final Speed of trip = 30km/h

TO FIND :-

• Average Speed for overall trip.

FORMULAE USED :-

• ${\boxed{\rm{Average\:Speed = \dfrac{Total\: Distance\:Covered} {Time\:Taken}}}}$.

How To solve

• We will take Distance as x the use the Formulae for Finding the Time.

• After Finding the time We will Use the Formulae written above.

Now,

Let the Distance Covered be x

$\rm{Time\:Taken\:while\:going\:School =\dfrac{Distance}{Speed}}$

$\rm{Time\:Take\:while\:going\:School =\dfrac{x}{20}}$

$\rm{Time\:Taken\:while\: returning\:home = \dfrac{x}{30}}$.

Therefore,

$\implies\rm{Total\: Distance\: travelled = x + x}$

$\implies\rm{Total\: Distance\: travelled = 2x}$

$\implies\rm{Total\:Time\:Taken =\dfrac{x}{20} + \dfrac{x}{30}}$

Now, Using the formulae.

$\implies\rm{Average\:Speed = \dfrac{Total\: Distance\:Covered} {Time\:Taken}}$

$\implies\rm{Average\:Speed = \dfrac{2x}{\dfrac{x}{20} +\dfrac{x}{30}}}$

• Taking LCM of 20 and 30 as 60

$\implies\rm{Average\:Speed = \dfrac{2x} {\dfrac{3x+2x}{60}}}$

$\implies\rm{\dfrac{2\times{60}}{5}}$

$\implies\rm{\dfrac{120}{5}}$

$\implies\rm{24km/h^{-1}}$.

Hence, The Average speed is 24km/h^-1