Question

A car travels 100 km at a speed.
of 20 km / her
Find
the speed at
which it should travel next 200km,
so that the
the average speed of a trip
is 25 km/hr.​

Answer 1

Topic :- Motion in straight line

$\maltese\:\underline{\textsf{\textbf{AnsWer :}}}\:\maltese$

• Distance travelled in first half (D₁) = 100 km
• Distance travelled in second half (D₂) = 200 km
• Speed of the car at first half (S₁) = 20 km/hr
• Speed of the car at second half (S₂) = ?
• Average speed = 25 km/hr
• Total distance travelled by the car = D₁ + D₂ = 100 + 200 = 300 km

$\footnotesize\longrightarrow\:\sf Average \: Speed = \dfrac{Total \: distance \: travelled}{Total \: time \: taken}$

$\tiny \qquad\qquad\qquad\dag\:\:\tt Time \: taken = \dfrac{Distance}{Speed}$

$\footnotesize\longrightarrow\:\sf Average \: Speed = \dfrac{Total \: distance \: travelled}{ \frac{ Distance \: (D_1)}{Speed (S_1)} + \frac{Distance \: (D_2)}{Speed (S_2)} }$

$\footnotesize\longrightarrow\:\sf 25 = \dfrac{300}{ \frac{100}{20} + \frac{200}{S_2} }$

$\footnotesize\longrightarrow\:\sf 25 = \dfrac{300}{ \frac{10}{2} + \frac{200}{S_2} }$

$\footnotesize\longrightarrow\:\sf 25 = \dfrac{300}{ 5 + \frac{200}{S_2} }$

$\footnotesize\longrightarrow\:\sf 25 = \dfrac{300}{ \frac{5S_2 + 200}{S_2} }$

$\footnotesize\longrightarrow\:\sf 25 = 300 \times \frac{S_2}{5S_2 + 200}$

$\footnotesize\longrightarrow\:\sf 25 = \frac{300S_2}{5S_2 + 200}$

$\footnotesize\longrightarrow\:\sf 25 (5S_2 + 200)= 300S_2$

$\footnotesize\longrightarrow\:\sf 125S_2 + 5000= 300S_2$

$\footnotesize\longrightarrow\:\sf 5000= 300S_2 - 125S_2$

$\footnotesize\longrightarrow\:\sf 5000= 175S_2$

$\footnotesize\longrightarrow\:\sf S_2 = \frac{5000}{175}$

$\footnotesize\longrightarrow\underline{ \boxed{\:\sf S_2 = 28.6 \: {km}^{ - 1} }}$

Answer 2

answer = 28.6 km/hr

( explanation is in the attachment)

hope it helps you ☺