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On Benz Circle three consecutive traffic lights change after 35,42,70 seconds respectively. If the lights are switched on at 2:00 P.M. sharp at what time will they change simultaneously?02:03:35 P.M02:03:42 P.M02:03:58 P.M02:03:30 P.M02:03:40 P.M

Question

On Benz Circle three consecutive traffic lights change after 35,42,70 seconds respectively. If the lights are switched on at 2:00 P.M. sharp at what time will they change simultaneously?02:03:35 P.M02:03:42 P.M02:03:58 P.M02:03:30 P.M02:03:40 P.M

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Solution

Para resolver esta pregunta, necesitamos encontrar el mínimo común múltiplo (MCM) de los tiempos en segundos en los que cambian las luces del semáforo. Los tiempos son 35, 42 y 70 segundos.

  1. Descomponemos cada número en sus factores primos:

    • 35 = 5 × 7
    • 42 = 2 × 3 × 7
    • 70 = 2 × 5 × 7
  2. Identificamos los factores primos únicos y tomamos el mayor exponente de cada uno:

    • 2: máximo exponente es 1 (de 42 y 70)
    • 3: máximo exponente es 1 (de 42)
    • 5: máximo exponente es 1 (de 35 y 70)
    • 7: máximo exponente es 1 (de 35, 42 y 70)
  3. Calculamos el MCM multiplicando estos factores:

    • MCM = 2^1 × 3^1 × 5^1 × 7^1 = 2 × 3 × 5 × 7 = 210

El MCM de 35, 42 y 70 es 210 segundos.

  1. Convertimos 210 segundos a minutos y segundos:

    • 210 segundos = 3 minutos y 30 segundos
  2. Sumamos este tiempo a la hora inicial de 2:00 P.M.:

    • 2:00 P.M. + 3 minutos y 30 segundos = 2:03:30 P.M.

Por lo tanto, las luces cambiarán simultáneamente a las 02:03:30 P.M. La respuesta correcta es:

02:03:30 P.M.

This problem has been solved

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