Question : A man travels 600 km by train at 80 km/hr, 600 km by ship at 30 km/hr, 500 km by aeroplane at 400 km/hr, and 300 km by car at 60 km/hr. What is the average speed (km/hr) for the entire distance?
Option 1: $56\frac{7}{27}$
Option 2: $63$
Option 3: $59\frac{7}{27}$
Option 4: $62\frac{7}{27}$
Correct Answer: $59\frac{7}{27}$
Solution :
$\text{Average speed}=\frac{\text{Total distance}}{{\text{total time}}}$
Total distance travelled = (600 + 600 + 500 + 300) km = 2000 km
Total time taken
= $\frac{600}{80}+\frac{600}{30}+\frac{500}{400}+\frac{300}{60}$
= $\frac{15}{2}+20+\frac{5}{4}+5$
= $\frac{30+80+5+20}{4}$
= $\frac{135}{4}$ hr
Average speed = $2000×\frac{4}{135}=\frac{8000}{135}$ km/hr = $\frac{1600}{27}=59\frac{7}{27}$ km/hr
Hence, the correct answer is $59\frac{7}{27}$ km/hr.
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