Answer:
\[{{V}_{1}}=30\,kmph\text{ }{{V}_{2}}=50\,kmph\]
\[{{V}_{1}}=30km/h\,\,{{V}_{2}}=50km/h\]
\[{{S}_{1}}=S\,\,km\,\,{{S}_{2}}=S\,\,km\]
Average speed = ?
We know that,
Average speed \[=\frac{total\,\,dis\tan ce}{total\,\,time}=\frac{2S}{t}\] ……(1)
How to get total time (t) = ?
Let\[{{t}_{1}}\]and \[{{t}_{2}}\]be the times taken by the body to cover AB and BC respectively.
Let us find the same.
We know, \[v=\frac{S}{t}\]or \[t=\frac{S}{v}\] ..….(2)
Applying (2), we get\[{{t}_{1}}=\frac{{{S}_{1}}}{{{v}_{1}}}=\frac{S}{30}=\frac{S}{30}hours\]
\[{{t}_{2}}=\frac{{{S}_{2}}}{{{v}_{2}}}=\frac{S}{50}=\frac{S}{50}hours\]
Total time taken (t)
\[=\frac{S}{30}+\frac{S}{50}=\frac{8S}{150}hours=\frac{9}{4}hours\]
And, total distance travelled\[=S+S=2S\,\,km\]
Substituting the above values in 1, we get
\[Average\,\,speed=\frac{Total\,\,dis\tan ce\,\,travelled}{Total\,\,time\,\,taken}\]
\[=\frac{2S}{{}^{8S}/{}_{150}}=\frac{150}{4}=37.5km/h\]
Thus, the average speed of the car for the whole journey is 37.5 kmph.
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