Question

Abus travelled from village A to village B at a speed of 40 km per hour. On the
return journey its speed was 60 km per hour. What is the average speed of the
bus during the entire journey?
(1) 50 km/h (2) 48 km/h (3) 46 km/h (4) 45 km/h​

Answer 1

Given :

• A bus travelled from village A to village B at a speed of 40 km per hour.

• On the return journey its speed was 60 km per hour.

To calculate :

• Average speed during the entire journey.

Calculation :

Let the distance from A to B be d km.

We know that,

$\bigstar \: \boxed{\sf {Average \: Speed = \dfrac{Total \: Distance}{Total \: time \: taken} }}$

$\underline{ \underline{ \sf \red {Calculating \: total \: distance \: \: :}} }$

Firstly it travels from A to village B and then it returns from B to A.

➠ Distance from A to B = d

➠ Distance from B to A = d

➛ Total Distance = Distance from A to B + Distance from B to A

➛ Total Distance = ( d + d ) km

➛ Total Distance = 2d km

$\underline{ \underline{ \sf \red{Calculating \: total \: time \: \: :}} }$

As we know that,

$\bigstar \: \boxed{\sf { Time = \dfrac{Distance}{Speed} }}$

Time taken to cover the distance from A to B (t₁):

➠ t₁ = $\sf { \dfrac{d}{40} }$ hrs

Time taken to cover the distance from B to A (t₂):

➠ t₂ = $\sf { \dfrac{d}{60} }$ hrs

➛ Total time = t₁ + t₂

➛ Total time = $\sf { \dfrac{d}{40} + \dfrac{d}{60} }$ hrs

➛ Total time = $\sf { \dfrac{3d + 2d}{120} }$ hrs

➛ Total time = $\sf { \dfrac{5d}{120} }$ hrs

➛ Total time = $\sf { \dfrac{1d}{24} }$ hrs

➛ Total time = $\sf { \dfrac{d}{24} }$ hrs

Now, substituting the values in the formula of average speed to find the average speed of the bus during the entire journey.

$\bigstar \: \boxed{\sf {Average \: Speed = \dfrac{Total \: Distance}{Total \: time \: taken} }}$

➛ Average speed = $\sf{ \dfrac{2d}{ \cfrac{d}{24} }}$ km/h

➛ Average speed = $\sf{ 2 \not{d} \times \dfrac{24}{\not{d}}}$ km/h

➛ Average speed = $\sf{ 2 \times 24 }$ km/h

➛ Average speed = 48 km/h

Therefore, average speed of the bus during the entire journey is 48 km/h. Option ⑵ is correct.

Answer 2

Assume distance from A to B = (x) km

From A to B, speed = 40 km/h

From B to A, speed = 60 km/h

We know,

v (bar) = (Total 's')/(Total 't')

and, t = s/v

So, t1 = x/40 h

t2 = x/60 h

∴ v (bar) = (x + x)/(x/40 + x/60) km/h

⇒ v (bar) = 2/(1/40 + 1/60) km/h

⇒ v (bar) = 2/(1/24) km/h

⇒ v (bar) = 24 × 2 km/h

⇒ v (bar) = 48 km/h.

So, average speed of the whole journey is 48 km/h (2).