Question

A body travel a distance of 10km with speed of 30 km /hr and then cover 40km with speed of 50km /hr find average speed

Answer 1

Given that :

• Distance traveled by the body = 10 km

• Speed = 30 km/hr

• Then, covered:

• Distance = 40 km, Speed = 50 km/hr

To Find :-

• The average speed of the body.

Solution :-

Given that,

 10 km takes 30 km/hr

 40 km takes 50 km/hr

$\bf Time \ taken = \dfrac{Distance }{Speed}$

Time taken to cover 10km = $\sf\dfrac{10}{30}$

                                             = $\sf\dfrac{1}{3}$ hours

Time taken to cover 40km = $\sf\dfrac{40}{50}$

                                              = $\sf\dfrac{4}{5}$

Total time taken = $\sf \dfrac{1}{3}+\dfrac{4}{5}$

                            = $\sf\dfrac{5+12}{3\times 5}$

                            = $\sf\dfrac{17}{15}$

Total distance = 10 + 40 = 50 km

$\bf Average \ speed = \dfrac{Total \ distance }{Total \ time \ taken }$

$\longrightarrow\sf Average \ speed = \dfrac{50}{\dfrac{17}{15}}$

                         $= \sf 50\times \dfrac{15}{17} \\\\ = \dfrac{750}{17}\\\\= \bf 44.12 \ km/hr$

Answer 2

Answer:

$\qquad \: \: \: \bigstar \: \underline{\:\large{\sf{For \: First \: \textit {10} \: km :}}}$

$\bullet\:\:\textsf{Distance = \textbf{10 km}}$

$\bullet\:\:\textsf{Speed at which the first 10 km distance was covered = \textbf{30 km/hr}}$

• As we know time equals distance divided by speed.

$\bullet\:\:\textsf{So, Time taken to cover first 20 km distance= 10/30 = \textbf{ 1 /3 hours}}$

$\qquad \: \: \: \bigstar \: \underline{\:\large{\sf{For \: next\: \textit {40} \: km :}}}$

$\bullet\:\:\textsf{Distance = \textbf{40 km}}$

$\bullet\:\:\textsf{Speed at which the first 40 km distance was covered = \textbf{50 km/hr}}$

$\bullet\:\:\textsf{So, Time taken to cover first 40 km distance= 40/50 = \textbf{ 4 /5 hours}}$

__________________...

Therefore, the total time taken by the body is :

$: \implies \textsf {Total time = Time taken to cover first 10 km distance + Time taken to cover next 40 km distance}$

$: \implies \sf Total \: time =\dfrac{1}{3} + \dfrac{4}{5}$

$: \implies \sf Total \: time = \dfrac{5 + 3 \times 4}{3 \times 5}$

$: \implies \sf Total \: time = \dfrac{5 + 12}{15}$

$: \implies \sf Total \: time = \dfrac{17}{15} \: hours$

__________________....

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\dashrightarrow\:\:\sf Average \: Speed = \dfrac{Total \: Distance}{Total \: Time \: taken}$

$\dashrightarrow\:\:\sf Average \: Speed = \dfrac{10 + 40}{ \frac{17}{15} }$

$\dashrightarrow\:\:\sf Average \: Speed = \dfrac{50}{ \frac{17}{15} }$

$\dashrightarrow\:\:\sf Average \: Speed = \dfrac{50 \times 15}{ 17 } \: \: \: \Bigg\lgroup \bf{\because Apply \: the \: Fraction \: rule : \dfrac{a}{\frac{b}{c}} = \frac{a \times c}{b} }\Bigg\rgroup$

$\dashrightarrow\:\:\sf Average \: Speed = \dfrac{750}{ 17 }$

$\dashrightarrow\:\: \underline{ \boxed{\textsf{ \textbf{Average \: Speed = 44.12 \:km/hr}}}}$

Therefore, the average speed will be: 44.12 km/h