Question : A person travels 600 km by train at 80 km/hr, 800 km by ship at 40 km/hr, 500 km by aeroplane at 400 km/hr, and 100 km by car at 50 km/hr. What is the average speed for the entire distance?
Option 1: $65\frac{5}{123}$ km/hr
Option 2: 60 km./hr.
Option 3: $60\frac{5}{123}$ km/hr
Option 4: 62 km./hr.
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Correct Answer: $65\frac{5}{123}$ km/hr
Solution :
Average speed = $\frac{total \;distance}{total \;time}$
Average speed = $\frac{600+800+500+100}{\frac{600}{80}+\frac{800}{40}+\frac{500}{400}+\frac{100}{50}} = \frac{2000\times 400}{12300}$
=$ \frac{8000}{123}$
= $65\frac{5}{123}$ km/hr
Hence, the correct answer is $65\frac{5}{123}$ km/hr.
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