Question

An public bus travels half of its journey with a speed of 40m/sec and other half with the speed of 30m/sec. Find its average speed?

Answer 1

let the distance is X meter , for half way (X/2) speed is 40 m/sec then time spent for it is. T1=X/2×40, T1= X/80 sec , and for another half way(X/2) speed is 30m/sec then time for it is T2=X/2×30 , T2= X/60 sec . average speed=total distance/total time,. here total distance is X meter and total time is T1+T2 ,. av. speed=X/T1+T2,. av. speed=X/(X/80+ X/60),. x is cancelled out then. av.speed =1/(1/80+1/60) after LCM. av. speed =1/(4+3/240). av. speed= 1/(7/240) , av. speed=240/7 , av. speed= 34.2 m/sec

Answer 2

Given:

Speed of bus during first half of journey,v₁= 40 m/s

Speed of bus during second half of journey,v₂= 30 m/s

To Find:

Average speed of bus

Solution:

We know that,

• If a body covers first half of a distance with speed v₁ and second half with speed v₂, then average speed of body S is given by,

$\pink{\boxed{\bf{S=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}}}$

$\rule{190}{1}$

Let the average speed of bus be S

So,

$\longrightarrow\rm{S=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}$

$\longrightarrow\rm{S=\dfrac{2\times40\times30}{40+30}}$

$\longrightarrow\rm{S=\dfrac{2400}{70}}$

$\longrightarrow\rm\green{S=34.29\ m/s}$

Hence, the average speed of public bus during journey is 34.29 m/s.