Question

Abdul, while driving to school, computes the average speed for his trip to be 20 Km/h.
On his return trip along the same route there is less traffic and the average speed is 30 Km/h.
What is the average speed for Abdul's trip?

Answer 1

Correct Question -

Abdul while driving to school computes the average speed of the trip to be 20 kmph .

On his return trip along the same route , there is less traffic and the average speed is 30 kmph .

What is the average speed for Abdul ' s trip ?

Solution -

See the attached diagram ....

In the above Question , the following information is given -

Abdul while driving to school computes the average speed of the trip to be 20 kmph .

On his return trip along the same route , there is less traffic and the average speed is 30 kmph .

So ,

The innitial average speed is 20 kmph .

The final average speed is 30 kmph .

Let the distance between Abdul ' s home and his school be D metres .

Total distance covered by Abdul = 2 D

We also know the following formula -

Speed = [ Total Distance Covered ] / [ Total time taken ]

So ,

20 = [ D ] / [ T 1 ]

=> T 1 = [ D ] / 20

30 = [ D] / [ T 2 ]

=> T2 = [ D ] / 30

Total time taken for the whole trip

=> T 1 + T 2

=> D / 20 + D / 30

=> ( 5 D ) / 60

Now , Similarly -

Average Speed = [ Total Distance Covered ] / [ Total time taken ]

=> Average speed

=> [ 2 D ] / [ ( 5 D / 60 )

=> 24 kmph .

Hence the average speed for Abdul ' s trip is 24 kmph ...

Answer 2

Given:-

• Average speed while driving to school = 20 km/h
• Average speed while returning = 30 km/h

To Find:

Average speed of Abdul’s trip.

We know,

AVERAGE SPEED =

• $\frac{2 {v}_{1}{v}_{2}}{{v}_{1} + {v}_{2}}$

where,

• $v_1$, $v_2$ = Speeds.

&

• $\frac{Total \ (s)}{Total \ (t)}$

where,

• s = Distance,
• t = Time.

Method 1:- (via Formula 1)

Avg. speed:-

$\frac{2 {v}_{1}{v}_{2}}{{v}_{1} + {v}_{2}}$

$\implies \frac{2 (20 km/h)(30 km/h)}{20 km/h + 30 km/h}$

$\implies \frac{2(600 km/h × km/h}{50 km/h}$

$\implies \frac{2 \times 60}{5} km/h$

$\implies 2 × 12 km/h$

$\implies 24 km/h \ (Solution)$

Method 2:- (via Formula 2)

Let distance covered by Abdul while going to school = x

∴ Return = x

Total distance = 2x

We know,

t = s/v

["t" resembles time, "s" shows distance and "v" displays speed]

Thus,

t′ = $\frac{x}{20 km/h}$

t″ = $\frac{x}{30 km/h}$

Total time = t′ + t″ = $\frac{x}{20 km/h} + \frac{x}{30 km/h}$

Putting the values,

$\frac{Total \ (s)}{Total \ (t)}$

$= \frac{2x \ km}{\frac{50x}{600} \ h}$

$= 24 km/h \ (Solution)$

∴ The Average Speed in Abdul's trip was of 24 km/h.

@Imperius