Question

A body cover a 1st half of its distance with speed V from the next half 1st half is covered with the speed of V and 2nd half is covered with the speed of 3V . Find the average speed of the total journeys..​

Answer 1

Given :

• A body cover a 1st half of its distance with speed V
• Speed for the next half 1st half is covered with the speed of V
• Speed for next 2nd half is covered with the speed of 3V

To find :

Average speed of total journey

Let :

Total distance covered = 4x

Understanding :

• The body cover 1st half distance ( that is 2x here) with speed = V
• The body then cover , 1st half of remaining distance ( that is x here ) with speed = V
• The body cover 2nd half ( that is x here) with speed = 3V

Now we will find time taken to cover each part , that will give us total time of journey.

Then using relationship between speed , time and distance , we will find average speed .

Formula used :

Distance = speed × time

Solution :

For 1st half of journey (2x) -

• Speed = V
• distance = 2x

Time ( t₁ ) = Distance ÷ speed

➝ t₁ = 2x ÷ V

_______________________________________________

For 2nd part of journey (2x) -

2nd part of journey is further sub-divided into 2 part, 1st half (x) & 2nd half (x)

For 1st part -

• Speed = V
• Distance = x

Time ( t₂ ) = Distance ÷ speed

➝ t₂ = x ÷ v

For 2nd part -

• Speed = 3V
• Distance = x

Time ( t₃ ) = Distance ÷ speed

t₃ = x ÷ 3V

_______________________________________________

Total time taken to complete journey = t₁ + t₂ + t₃

$\sf \implies \: t_1 + t_2 + t_3 \: = \dfrac{2x}{V} \: + \: \dfrac{x}{V} \: + \: \dfrac{x}{3V} \\ \\ \sf \implies \: t_1 + t_2 + t_3 \: = \dfrac{(2x \times 3) + (x \times 3) + (x \times 1)}{3V} \\ \\ \sf \implies \: t_1 + t_2 + t_3 \: = \: \dfrac{6x + 3x + x}{3V} \\ \\ \sf \implies \: t_1 + t_2 + t_3 \: = \: \dfrac{10x}{3V}$

_______________________________________________

For complete journey

• Total distance = 4x
• Total time = 10x/3V

$\sf \implies \: Average \: speed \: = \: \dfrac{ Total \: distance }{Total \: time} \\ \\ \sf \implies \: Average \: speed \: = \: \dfrac{4x}{ \dfrac{10x}{3 V } } \\ \\ \sf \implies \: Average \: speed \: = 4x \times \dfrac{3 V }{10x} \\ \\ \sf \implies \: Average \: speed \: = \dfrac{6V }{5}$

_______________________________________________

ANSWER :

Average speed = 6V ÷ 5 = 1.2V