Question : A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of their time taken is 14 hours. Then A's speed is equal to:
Option 1: 3 km/hr
Option 2: 4 km/hr
Option 3: 5 km/hr
Option 4: 7 km/hr
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Correct Answer: 4 km/hr
Solution :
Let the speed of A = $x$ km/hr
and the speed of B = $(7-x)$ km/hr
So, the time taken by A and B to walk 24 km are ($\frac{24}{x}$) hours and ($\frac{24}{7 - x}$) hours, respectively.
Now $(\frac{24}{x}) + (\frac{24}{7-x}) =14$
$⇒ 24(7-x)+24x = 14x(7-x)$
$⇒ 168 - 24x+24x = 98x-14x^{2}$
$⇒ 14x^{2}-98x+168 = 0$
$⇒ x^{2}-7x+12 = 0$
$⇒ (x-4)(x-3) = 0$
$⇒x = 3$ or $x = 4$
Since A is faster than B, A's speed is equal to 4 km/hr.
Hence, the correct answer is 4 km/hr.
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