Question : A person goes from J to K at a speed of 55 km/hr. He comes back from K to J at a certain speed. If his average speed is $\frac{660}{17}$ km/hr, then what was his speed while moving from K towards J?
Option 1: 24 km/hr
Option 2: 38 km/hr
Option 3: 30 km/hr
Option 4: 42 km/hr
Correct Answer: 30 km/hr
Solution :
Speed, $S_1$ = 55 km/hr
Average speed = $\frac{660}{17}$ km/hr
Let $S_2$ be the required speed.
Average speed = $\frac{2S_1S_2}{S_1+S_2}$
$⇒\frac{660}{17}=\frac{2×55×S_2}{55+S_2}$
$⇒\frac{660}{17}=\frac{110×S_2}{55+S_2}$
$⇒\frac{6}{17}=\frac{S_2}{55+S_2}$
$⇒330 + 6S_2 = 17S_2$
$⇒330 = 11S_2$
$\therefore S_2 = 30$ km/hr
Hence, the correct answer is 30 km/hr.
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