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A is faster than B, A and B each walk 24 km. the sum of their speeds is 7 km/hr and sum of times taken by them is 14 hours Then A's speed is equal to

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km / hr

km / hr

km / hr

km / hr

answer is B.

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Detailed Solution

Given,
A is faster than B
Suppose the speed of A =x
And the speed of B =y.
Given in the question, the sum of speed =7.

x + y = 7 km / hr

y = 7 - x

Since,
Time=distance/speed, so,
The time taken by A to cover 24 km = 24/x………(1)
The time taken by B to cover 24 km = 24/y…………(2)
Sum of times taken by them is 14 hours. So,

\Rightarrow 14 = \frac{24}{x} + \frac{24}{(7 - x)}

\Rightarrow 24 (7 - x) + 24 x = 14 x (7 - x)

\Rightarrow 168 = 98 x - 14 x^{2}

\Rightarrow 14 x^{2} - 98 x + 168 = 0

\Rightarrow x^{2} - 7 x + 12 = 0

\Rightarrow (x - 3) (x - 4) = 0

\Rightarrow x = 3 or 4

As, A is faster than B.
So, A's speed is equal to

4 km / hr

while B’s speed is 3 km/hr.
Correct option is 2.

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