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A. Consider a race of n cars that leave the same place and with constant speeds, but different from each other. If at a given moment the distance between each car and the one in front of it everyone has the same distance, at what other point in the race will this happen? Justify your answer. B. What is the value of the ratio between the speed of the fastest in relation to that of the slowest?

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Answer to a math question A. Consider a race of n cars that leave the same place and with constant speeds, but different from each other. If at a given moment the distance between each car and the one in front of it everyone has the same distance, at what other point in the race will this happen? Justify your answer. B. What is the value of the ratio between the speed of the fastest in relation to that of the slowest?

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**A.** Vamos considerar que no momento inicial, a distância entre cada carro e o da frente dele é a mesma. Isso significa que a diferença de distância percorrida por cada carro também é a mesma.

Se a velocidade do carro mais rápido é

v_1

, a do segundo carro é

v_2

, e assim por diante até a velocidade do carro mais lento

v_n

, a distância percorrida por cada um deles será igual em um certo momento.

Se após um tempo

t

a distância entre eles for a mesma novamente, isso significa que a diferença de distância percorrida por cada carro continua a mesma. Portanto, no novo momento em que isso acontecer, cada carro terá percorrido uma distância maior, mas a relação de distância entre eles será a mesma.

**Resposta:** Em outro momento da corrida em que a distância entre cada carro e o da frente dele seja a mesma, será quando esta relação de distância percorrida por cada um se mantiver constante.

**B.** A relação entre a velocidade do carro mais rápido e a do mais lento pode ser encontrada pela razão entre suas velocidades.

Se a velocidade do carro mais rápido é

v_1

e a do mais lento é

v_n

, então a relação será:

\frac{v_1}{v_n}

**Resposta:** A relação entre a velocidade do carro mais rápido em relação à do mais lento é

\frac{v_1}{v_n}

.

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