Question

A car with half the distance of 40 km/h of your journey and half the distance of v km/h. find out the value the car if the average speed as 48 km/h.

Answer 1

Correct Question:-

⟼ A car covered first half of the journey with 40 km/h and other half with v km/h. Find out the value of 'v', if the average speed of car during journey is 48 km/h.

Given:

➺ A car travelled first half of the journey with speed 40 km/h and other half with v km/h

➺ Average speed of journey is 48 km/h

To Find:

• Value of 'v'

Solution:

We know that,

If a body covers first half of a distance with speed v₁ and second half with speed v₂, then

$\boxed{\tt{Average\:Speed=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}}$

So,

$\tt{48=\dfrac{2\times40\times v}{40+v}}$

$\tt{48(40+v)=80\times v}$

$\tt{1920+48v=80v}$

$\tt{80v-48v=1920}$

$\tt{32v=1920}$

$\tt{v=\dfrac{1920}{32}}$

$\tt\pink{v=60\:km/hr}$

Hence, the value of v is 60 km/hr.

Answer 2

Solution :

⏭ Given:

✏ A car covered first half of total distance with velocity 40kmph and second half of total distance with velocity v kmph.

✏ Average velocity of car is 48kmph.

⏭ To Find:

✏ Value of v

⏭ Concept:

✏ Average velocity is defined as ratio of total distance covered by body to total time taken.

⏭ Formula derivation:

✏ Let body covers first d/2 of total distance with velocity v1 in time t1 and second d/2 of total distance with velocity v2 in time t2.

✏ Total distance covered by body = d

$\mapsto \sf \: v_{av} = \frac{ \frac{d}{2} + \frac{d}{2} }{ \frac{d}{2v_1} + \frac{d}{2v_2} } \: \: ( \because \: time= \frac{distance}{velocity} ) \\ \\ \mapsto \sf \: v_{av} = \frac{ 2 \times \cancel{d} \times v_1v_2}{ \cancel{d}(v_1 + v_2)} \\ \\ \mapsto \underline{\boxed{ \bold{ \sf{ \orange{v_{av} = \frac{2v_1v_2}{v_1 + v_2}}}}}} \: \star$

⏭ Calculation:

$\mapsto \sf \: 48 = \frac{2 \times 40 \times v}{40 + v} \\ \\ \mapsto \sf \: 1920 + 48v = 80v \\ \\ \mapsto \sf \: 32v = 1920 \\ \\ \mapsto \: \purple{\underline{ \boxed{ \bold{ \sf{ \red{v = 60 \: kmph}}}}}} \: \green{ \clubsuit}$