Answer:
The speed of the champion (v1) = 6 km/h.
Step-by-step explanation:
v1: velocity of the champion
t1: the amount of time the champion completed the race
v2: velocity of the 15th winner
t2: the amount of time the 15th winner completed the race
S: the distance
We have the equation: S = v1.t1 = v2.t2 (1)
The champion ran 2 km/h faster than the 15th winner, so:
v2 = v1 - 2 (2)
The champion finished the race 30 minutes (or half an hour) before the 15th winner, so:
t2 = t1 + 0.5 (3)
From (1), (2) and (3), we have:
v1×t1 = (v1-2)×(t1+0.5)
<=> v1×t1 = v1×t1 + 0.5×v1 - 2×t1 - 2×0.5
<=> 0.5×v1 - 2×t1 - 2×0.5 = 0
<=> 0.5×v1 = 2×t1 + 1
<=> 0.5×v1 - 1 = 2×t1
<=> t1 = (0.5×v1 - 1)/2 [4]
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As S = v1×t1 = 6 and t1 = (0.5×v1 - 1)/2, we have:
v1×(0.5×v1 - 1)/2 = 6
<=> v1×(0.5×v1 - 1) = 2×6 = 12
<=> 0.5 v1^2 - v1 = 12
<=> v1^2 - 2×v1 = 24
<=> (v1^2 - 2×v1 + 1) = 25
<=> (v1 - 1)^2 = 25
<=> v1 - 1 = 5
=> v1 = 5 + 1 = 6 (km/h)
