Question : A man covers half part of a certain distance at 25 km/hr. He covers 40% 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: $\frac{650}{37}$ km/hr
Option 2: $\frac{540}{37}$ km/hr
Option 3: $\frac{600}{37}$ km/hr
Option 4: $\frac{480}{37}$ km/hr
Correct Answer: $\frac{600}{37}$ km/hr
Solution :
Let the total distance be 100 km.
For the first part of the journey:
Distance = $\frac{100}{2}$ = 50 km
Speed = 25 km/hr
$\therefore$ Time taken to cover half the distance = $\frac{50}{25}$ = 2 hr
So, the remaining distance = 50 km
For the second part of the journey:
Distance = 40% of the remaining distance = $\frac{40}{100}×50$ = 20 km
Speed = 8 km/hr
$\therefore$ Time taken to cover 40% of the remaining distance = $\frac{20}{8}$ = $\frac{5}{2}$ hr
For the third part of the journey:
Distance = 60% of the remaining distance = $\frac{60}{100}×50$ = 30 km
Speed = 18 km/hr
$\therefore$ Time taken to cover 60% of the remaining distance = $\frac{30}{18}$ = $\frac{5}{3}$
Now, the average speed = $\frac{\text{Total distance}}{\text{Total time}}$
= $\frac{100}{2+\frac{5}{2}+\frac{5}{3}}$
= $\frac{100}{\frac{37}{6}}$
= $\frac{600}{37}$ km/hr
Hence, the correct answer is $\frac{600}{37}$ km/hr.
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