Question

A particle travels the first half of its total distance along a straight line with a speed 'v'kmph and the next
half, with a speed of 60 kmph. If the average speed for the journey is 40 kmph, the value of 'v' is
a) 50 kmph
b) 30 kmph
c) 20 kmph
d) 35 kmph [ ]​

Answer 1

${\huge{\boxed{\sf{\green{❥✰Question✰}}}}}$

• A particle travels the first half of its total distance along a straight line with a speed 'v'kmph and the next
• half, with a speed of 60 kmph. If the average speed for the journey is 40 kmph, the value of 'v' is
• a) 50 kmph
• b) 30 kmph
• c) 20 kmph
• d) 35 kmph [ ]​

$\huge\star\underline{\mathtt\orange{❥a} \mathfrak\blue{n } \mathbb\purple{ Տ} \mathbb\pink{wer}}\star\:$

• 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.

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

${Distance+Distance}{Time_1+Time_2}\\\\\\:\implies\sf Average\:Speed=\dfrac{Distance+Distance}{\frac{Distance}{Speed_1}+\frac{Distance}{Speed_2}}\\\\\\:\implies\sf 40=\dfrac{D+D}{\frac{D}{v}+\\\frac{D}{60}}\\\\\\:\implies\sf 40=\dfrac{2D}{\frac{60D+vD}{60v}}\\\\\\:\i\\mplies\sf 40 = \dfrac{2D \times 60v}{60D +vD}\\\\\\:\implies\\\sf 40 = \dfrac{2D\times 60v}{D(60+v)}\\\\\\:\implies\sf 40 = \dfra$

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

Value of v (i.e. 1st Half Speed) is 30 km/hr