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

Question

Question : A car can finish a certain journey in 10 hours at a speed of 42 km/hr. In order to cover the same distance in 7 hours, the speed of the car (km/hr) must be increased by:

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Answer 1

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 $(\frac{24}{x}) + (\frac{24}{7 - x}) = 14$
$\Rightarrow 24 (7 - x) + 24 x = 14 x (7 - x)$
$\Rightarrow 168 - 24 x + 24 x = 98 x - 14 x^{2}$
$\Rightarrow 14 x^{2} - 98 x + 168 = 0$
$\Rightarrow x^{2} - 7 x + 12 = 0$
$\Rightarrow (x - 4) (x - 3) = 0$
$\Rightarrow x = 3$ 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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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/hrOption 2: 4 km/hrOption 3: 5 km/hrOption 4: 7 km/hr

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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