Question

Example 4 A car travelled the first half of its journey at 40 km/h and the next half at 60 km/h. Find the average speed of the car over the whole journey.


Answer with full Explanation.​

Answer 1

Answer:

here this is answer

Explanation:

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Answer 2

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Given :- }}}}}}}\end{gathered}$

☆Speed of the car in first half of its journey = 40 km/h

☆ Speed of the car in next half of its journey = 60 km/h

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:To find \: :- }}}}}}}\end{gathered}$

✡ The average speed of the car over the whole journey.

${\large{\underline{\underline{\maltese{\textsf{\textbf{\: Using \: formula : - }}}}}}}$

$➵ \: \sf Average \: speed = \large \: \frac{total \: distance \: travelled}{total \: time \: taken }$

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\: Solution \: :- }}}}}}}\end{gathered}$

➵ Let the total distance travelled be 2x

$➵ ∴ \sf \: Total \: time \: taken = \large \frac{x}{40} + \frac{x}{60}$

$\clubsuit\: \: \sf\bold{\red{As \: we \: know \: that :- }}$

$➵ \: \sf Average \: speed = \large \: \frac{total \: distance \: travelled}{total \: time \: taken }$

$➵ \: \sf Average \: speed = \large \frac{2x}{\frac{x}{40} + \frac{x}{60} }$

$➵ \: \sf Average \: speed = \large \frac{2x} { \frac{3x + 2x}{120} } \: \red{ [L.C.M]}$

$➵ \: \sf Average \: speed = \large \frac{2x}{ \frac{5x}{120} }$

$➵ \: \sf Average \: speed = \large 2x \: \times \frac{120}{5 x}$

$➵ \: \sf Average \: speed = {\sf {2x \times {\dfrac{{\cancel{{120}}^{24}}}{{\cancel{{5 }}^1{x}}}}}}$

$➵ \: \sf Average \: speed = \large 2x \times \frac{24}{x}$

$➵ \: \sf Average \: speed = {\sf{~ ~\dfrac{2\cancel{x}~×~24}{\cancel{x}}}}$

$➵ \: \sf Average \: speed = 2 × 24$

$➵ \: \sf Average \: speed = 48 km/hr$

∴ Average speed of the car over the whole journey = 48 km / hr

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Extra important formula :-

$\bigstar \sf \: Distance \: Formula :-$

$\begin{gathered}\mapsto \sf\bold{{Distance =\: Speed \times Time}}\\\end{gathered}$

$\bigstar \sf Time \: Formula : -$

$\begin{gathered}\mapsto \sf\bold{{Time =\: \dfrac{Distance}{Speed}}}\\\end{gathered}$

$\bigstar \sf Speed \: Formula : -$

$\mapsto \sf\bold{{Speed =\: \dfrac{Distance}{Time}}}$

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Hope it helps :)