Question

Dalam suatu 6 km larian amal, beza masa yang digunakan

Answer 1

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)