Question : A man covers half part of a certain distance at 15 km/hr. He covers 40 percent of the remaining distance at the speed of 12 km/hr and covers the rest of the distance at the speed of 21 km/hr. What is his average speed for the entire journey?
Option 1: $\frac{140}{9}$ km/hr
Option 2: $15$ km/hr
Option 3: $\frac{164}{9}$ km/hr
Option 4: $\frac{139}{9}$ km/hr
Correct Answer: $\frac{140}{9}$ km/hr
Solution :
Let the total distance be $x$.
A man covers half part of a certain distance at 15 km/hr.
Time to cross half the distance = $\frac{\frac{x}{2}}{15}=\frac{x}{30}$
He covers 40% of the remaining distance at the speed of 12 km/hr.
Time taken = $\frac{\frac{40}{100}×\frac{x}{2}}{12}=\frac{x}{60}$
He covers the rest of the distance at the speed of 21 km/hr.
Time taken to cover the remaining distance = $\frac{\frac{60}{100}×\frac{x}{2}}{21}=\frac{x}{70}$
So, the average speed
$=\frac{\text{Total distance}}{{\text{Total time}}}=\frac{x}{\frac{x}{30}+\frac{x}{60}+\frac{x}{70}}=\frac{x}{\frac{27x}{420}}=\frac{420}{27}=\frac{140}{9}$ km/hr
Hence, the correct answer is $\frac{140}{9}$ km/hr.
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