Question

A truck travels some distance with the constant speed of 30km h-1 and returns back with the constant speed of 40km h-1 . Calculate the average speed of the truck .

Answer 1

Given that the truck travels some distance with a constant speed of 30 km/hr.

Let us assume that the truck starts from point A with a speed of 30 km/hr to point B. (From A to B speed = 30 km/hr.)

Also given in question that, truck returns back with a constant speed of 40 km/hr.

Now, from point B to point A, it travels with a speed of 40 km/hr.

Let us assume that the truck travels a distance of x km.

So, From point A to B it travels x distance. Similarly, from B point to A point, it travels x distance.

$\implies$ Total distance covered by truck = 2x

$\sf{Time=\dfrac{Distance}{Speed}}$

From point A to point B:

$\sf{t1=\dfrac{x}{30}}$

From point B to point A:

$\sf{t2=\dfrac{x}{40}}$

Total time taken by truck = t1 + t2

= x/30 + x/40

= (4x + 3x)/120

= 7x/120

We have to find the Average Speed of the truck.

Average speed is defined as total distance covered by total time taken.

Therefore,

$\sf{Average\:speed=\dfrac{Total\: distance\: covered}{Total\:time\:taken}}$

$\implies\:\sf{\dfrac{2x}{\frac{7x}{120}}}$

$\implies\:\sf{\dfrac{2x(120)}{7x}}$

$\implies\:\sf{34.28\:km/hr}$

Short Method

Given speed 30 km/hr and 40 km/hr.

Take S1 = 30 km/hr and S2 = 40 km/hr

Average speed = (Total distance covered)/(Total time taken)

= (2 × 30 × 40)/(30 + 40)

= 2400/70

= 34.28 km/hr

Answer 2

GiveN :-

A truck travels some distance with the constant speed of 30 km/h and returns back with the constant speed of 40 km/h.

TO DeterminE :-

The average speed of the truck.

AcknowledgemenT :-

$\bigstar\ \sf{Average\ speed=\dfrac{Total\ distance\ covered}{Total\ time\ taken}}$

SolutioN :-

Let the distance be x km when the truck moves from(say A to B).

A/q, it travels x km again while travelling from B to A.

We know,

Time = Distance/Speed

Now,

Time taken while moving from A to B = x/30 hours

Time taken while moving from B to A = x/40 hours

$\rule{200}{2}$

◙ Total distance covered = x + x = 2x

◙ Total time taken = $\sf{\dfrac{x}{30}+\dfrac{x}{40} }$ = $\sf{\dfrac{4x+3x}{120} }$ = $\sf{\dfrac{7x}{120}}$

◙ Average speed = $\sf{2x \div \dfrac{7x}{120} =2x \times \dfrac{120}{7x} =\dfrac{240x}{7x} =\dfrac{240}{7} }$ = 34.28 m/s  

Therefore, the average speed of the truck in the whole journey is 34.28 m/s.