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[sri]

sri

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This should be an easier one. The earlier one is still open though.

Whenever A and B compete in a 100 meter race, A always wins by 5 meters. So in order to make the competition even, A and B then run a race where A stands 5 meters behind B and they race to the same finishing line 100 meters from where B is standing. Both A and B run with the same speed as they did earlier. Who is going to win the race now and why?

[bn pradeep]

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A is going to win.
v_a * t = 100
v_b * t = 95

v_a/v_b = 100/95

2nd case

v_a * t_a = 105
v_b * t_b = 100

t_a/t_b = (105/100) * (v_b/v_a)
                           t_a =  0.9975 * t_b

[sri]

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Good show!

But can we provide a solution without using the math? Especially without having to calculate velocity? Only using logic?

[bn pradeep]

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The first case implies that B is slower than A. The second case essentially means A has to cover 5 more meters (from 100 to 105) in the time B covers 5 meters (95 to 100). Since B is slower he will take more to time to cover the 5 meters.