question_answer

A car travels the first half of a distance between two places at a speed of 30 km/h and the second half of the distance at 50 km/h. Find the average speed of the car for the whole journey.

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.