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andreyandreev
1 month ago
5

Dos agricultores, padre e hijo, tardan 2 horas entre los dos arar un campo. Si solo el padre tarda 6 horas. ¿Cuanto tardara el h

ijo?
Mathematics
1 answer:
Leona [12.6K]1 month ago
8 0

Answer:

El hijo tardará solo 3 horas en completar el arado del terreno.

Detailing the process:

Sabemos que ambos tardan 2 horas en conjunto para labrar el campo, mientras que el padre lo hace solo en 6 horas.

Queremos determinar cuánto tiempo le llevará al hijo si trabaja solo.

Consideremos que el área del campo es x.

La tasa de trabajo conjunta de ellos es x/2.

La tasa de trabajo del padre es x/6, siendo y el tiempo que el hijo tarda. Por lo tanto, la tasa del hijo es x/y.

Sumando las tasas del padre y del hijo se obtiene la tasa de trabajo total. Así que tenemos:

x/6 + x/y = x/2.

Al despejar x, obtenemos 1/6 + 1/y = 1/2.

1/y = 1/2 - 1/6.

1/y = 1/3.

Por lo tanto, y resulta ser 3.

El hijo tardará 3 horas en labrar el campo.

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