Question

A motorcyclist drivers 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

Answer 1

$\sf\fbox{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Answer\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bold\pink{Given :}$

$\sf {Speed \: of \: motorcycle \: from \: A \: to \: B = 30 \: km/h}$

$\sf {Speed \: of \: motorcycle \: from \: B \: to A \: = 20 km/h}$

$\bold\pink{To \:Find :}$

$\sf{Average \: Speed = ?}$

$\bold\pink{Concept:}$

Formula to be used,

$\small\underline{\boxed{\sf\;\;Average \:Speed = \dfrac{Total \: distance \: covered}{Total \: time \: taken}}}$

$\bold\pink{Solution :}$

$\sf{Let \: the \: distance \: covered \: is \: x}$

$\sf{Total \: distance \: covered = x + x = 2x}$

$\sf{Time \: taken \: from \: A \: to \: B = \dfrac{x}{30}}$

$\sf{Time \: taken \: from \: B \: to \: A = \dfrac{x}{20}}$

$\sf{Total \: time \: taken, t = \dfrac{x}{30} +\dfrac{x}{20} = \dfrac{5x}{60}}$

$\sf{Now,}$

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

$\sf{ \implies Average \: Speed = \dfrac{2x × 60}{5x}}$

$\sf{ \implies Average \: Speed = 24 km/h}$

$\sf{Hence, the \: Average \: Speed \: is \: 24 km/h}$

Answer 2

Let, distance between A to B = (x) km

First speed = 30 km/h

Second speed = 20 km/h

We know, t = s/v

Time taken from A to B:- (let ‘T’)

$T = \frac{x}{v_1} = \frac{x}{30} h$

Time taken from B to A:- (let ‘t’)

$t = \frac{x}{v_2} = \frac{x}{20} h$

Now we know,

$\boxed{v_{av} = \frac{Total \ distance}{Total \ time}}$

∴ $v_{av} = \frac{x + x}{T + t}$ km/h

⇒ $v_{av} = \frac{2x}{\frac{x}{30} + \frac{x}{20}}$ km/h

⇒ $v_{av} = \frac{2x}{\frac{2x + 3x}{60}}$ km/h

⇒ $v_{av} = \frac{2x \times 60}{5x}$ km/h

⇒ $v_{av} = 2 \times 12$ km/h

⇒ $v_{av} = 24$ km/h

ALITER:-

We know,

$\boxed{v_{av} = \frac{2ab}{a + b}}$

where, a and b are speed values given in the question.

Putting the values,

$v_{av} = \frac{2 \times 30 \times 20}{30 + 20}$ km/h

⇒ $v_{av} = \frac{2 \times 30 \times 20}{50}$ km/h

⇒ $v_{av} = 2 \times 2 \times 6$ km/h

⇒ $v_{av} = 24$ km/h (Answer).

NECESSARY TO KNOW:-

Average speed ≠ (v + u)/2

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