Question

EXAMPLE 1.23: A motorcyclist drives from A to B with a uniform speed of 30 km h and returns back
with a speed of 20 km h. Find its average speed.


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Answer 1

Answer:

• Average speed of motorcyclist is 24  km/h .

Explanation:

Given that,

Motorcycle drives from A to B with a uniform speed of 30 km/h , and returns back with a speed of 20 km/h

We need to find,

Average speed of Motorcyclist

so,

Let Distance between A and B be x  km

Using formula : time = distance/speed

and

Considering the journey from A to B

Let, t₁ be the time taken by motorcyclist to travel from A to B

then,

→ t₁ = x / 30  hrs

Considering the returning journey from B to A

Let, t₂ be the time taken by motorcyclist to travel from B to A

then,

→ t₂ = x / 20  hrs

Calculating total time taken for travelling A to B and B to A by motorcyclist

Let, total time taken by motorcyclist be t

then,

→ t = t₁ + t₂

→ t = x/30  +  x/20     hrs

→ t = ( 2 x + 3 x ) / 60    hrs

→ t = 5 x / 60     hrs

→ t = x / 12   hrs

Now,

Calculating average speed

Using formula

→ Av. speed = total distance covered / total time taken

→ Av. speed = ( x + x ) / ( x / 12 )

→ Av. speed = 2 x / ( x / 12 )

→ Av. speed = ( 2 x ) ( 12 / x )

→ Av. speed = 24  km/h

Therefore,

• Average speed of motorcyclist is 24 km/h .

Answer 2

Explanation:

Let distance between A and B is D

Then, time taken by motorcyclist with uniform speed 30 km/h ,T₁ = distance/speed = D/30 hrs

Again, they return with uniform speed 20 km , so time taken by motorcyclist , T₂ = D/20 hrs

Now, average speed of motorcyclist = total distance/total time taken

= (D + D )/(D/30 + D/20) km/h

= 2 × 30 × 20/(30 + 20) km/h

= 24 km/h

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