Question

a particle travels the first half of its total distance along the straight line with a speed 'v' kmph and the next half with a speed of 60kmph . if the average speed for the journey is 40kmph, the value'v' is

Answer 1

Answer:

Given:

1st half of distance is travelled with v , 2nd half with 60 km/hr . Average speed for whole journey is 40 km/hr

To find:

Value of v

Concept:

Average speed is defined as the ratio of total distance to the total time taken .

Calculation:

Let distance for each half be d.

$avg. \: v = \dfrac{total \: distance}{total \: time}$

$= > 40 = \dfrac{2d}{ (\frac{d}{v} + \frac{d}{60} )}$

Cancelling similar terms :

$= > 40 = \dfrac{2}{ (\frac{1}{v} + \frac{1}{60} )}$

$= > 40 = \dfrac{2}{( \frac{60 + v}{60v}) }$

$= > 40 = \dfrac{2 \times (60v)}{(60 + v)}$

$= > 60 + v = 3v$

$= > 2v = 60$

$= > v = 30 \: km {hr}^{ - 1}$

So final answer :

Value of v is 30 km/hr

Answer 2

Answer:

• First Half Speed = v km/hr
• Next Half Speed = 60 km/hr
• Average Speed = 40 km/hr
• Let the Distance travelled be D in each Half of Journey.

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf Average\:Speed=\dfrac{Total\: Distance}{Total\:Time}\\\\\\:\implies\sf Average\:Speed=\dfrac{Distance+Distance}{Time_1+Time_2}\\\\\\:\implies\sf Average\:Speed=\dfrac{Distance+Distance}{\frac{Distance}{Speed_1}+\frac{Distance}{Speed_2}}\\\\\\:\implies\sf 40=\dfrac{D+D}{\frac{D}{v}+\frac{D}{60}}\\\\\\:\implies\sf 40=\dfrac{2D}{\frac{60D+vD}{60v}}\\\\\\:\implies\sf 40 = \dfrac{2D \times 60v}{60D +vD}\\\\\\:\implies\sf 40 = \dfrac{2D\times 60v}{D(60+v)}\\\\\\:\implies\sf 40 = \dfrac{2 \times 60v}{60 + v}\\\\\\:\implies\sf 40(60 + v) = 2 \times 60v\\\\\\:\implies\sf 60 + v = 3v\\\\\\:\implies\sf 60 = 3v - v\\\\\\:\implies\sf 60 = 2v\\\\\\:\implies\sf \dfrac{60}{2} = v\\\\\\:\implies\underline{\boxed{\sf v = 30 \:km/hr}}$

⠀

$\therefore\:\underline{\textsf{Value of v (i.e. 1st Half Speed) is \textbf{30 km/hr}}}.$