Answer:
Time
taken to travel, \[{{t}_{1}}=0.5h,\]
\[{{t}_{1}}=1h,{{t}_{3}}=2h\]
\[t={{t}_{1}}+{{t}_{2}}+{{t}_{3}}\]
\[=0.5+1+2=3.5h\]
Speeds,\[{{\upsilon
}_{1}}=30\text{km/}h,{{\upsilon }_{2}}=25\,\text{km}/h,{{\upsilon }_{3}}=40\text{km/h}\]
Distances,
\[{{s}_{1}}={{\upsilon }_{1}}\times {{t}_{1}}=30\times 0.5=15\,km\]
\[{{s}_{2}}={{\upsilon
}_{2}}{{t}_{2}}=25\times 1=25\,km\]
\[{{s}_{3}}={{\upsilon
}_{3}}{{t}_{3}}=40\times 2=80\,km\]
\[s={{s}_{1}}+{{s}_{2}}+{{s}_{3}}\]
\[=15+25+80=120\,\text{km}\]
Average
speed\[\text{=}\frac{\text{Total}\,\text{distnace}}{\text{Total}\,\text{time}}\]
\[\text{=}\frac{\text{s}}{\text{t}}=\frac{120}{3.5}=34.3\,\text{km/h}\]
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