Question : A man covers half part of a certain distance at 35 km/hr. He covers 40 percent of the remaining distance at the speed of 8 km/hr and covers the rest of the distance at the speed of 18 km/hr. What is his average speed for the entire journey?
Option 1: $\frac{920}{47}$ km/hr
Option 2: $\frac{680}{47}$ km/hr
Option 3: $\frac{840}{47}$ km/hr
Option 4: $\frac{760}{47}$ km/hr
Correct Answer: $\frac{840}{47}$ km/hr
Solution :
Let the distance be D km.
According to the question,
Distance at 35 km/hr, he covers = $\frac{1}{2}$ × D
At 8 km/hr, he covers 40% of $\frac{1}{2}$ × D = $\frac{1}{5}$D
The rest of the distance = D – $\frac{1}{2}$D – $\frac{1}{5}$D = $\frac{3}{10}$D, he covers at 18 km/hr
So, total time = $\frac{\frac{1}{2} × D}{35} + \frac{\frac{1}{5} × D}{8} + \frac{\frac{3}{10} × D}{18} = \frac{47D}{840}$
⇒ Average speed $=\frac{\text{Distance}}{\text{Time}} = \frac{D}{\frac{47D}{840}} = \frac{840}{47}$ km/hr
Hence, the correct answer is $\frac{840}{47}$ km/hr.
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