Agustín y Bárbara salen al mismo tiempo y del mismo lugar, por el mismo camino. Agustín camina a 5km/h y Bárbara a 3km/h. Luego de recorrer 7km, Agustín emprende el regreso, ¿a qué distancia de la partida se encuentra con Bárbara? Si en el momento del encuentro también Bárbara emprende el regreso, ¿cuántos minutos después que Agustín llega Bárbara al punto de partida?

Answers

Answer 1

Answer:

Ok, primero Agustín camina a 5km/h.

Cuando el recorre 7km, el regresa.

El tiempo en el que sucede esto es a:

7km/5km/h = 1.4 h

La ecuación para Agustín es:

A(t) = 5km/h*t                                     para  0h ≤ t  ≤ 1.4h           (ida)

A(t) = 7km -  5km/h*(t - 1.4h)              para 1.4h ≤ t.                     (vuelta)

Hacemos lo mismo para Barbara:

7km/3km/h = 2.5h

La ecuación para ella es:

B(t) = 3km/h*t                                    para 0h ≤ t  ≤ 2.5h              (ida)

B(t) = 7km -  3km/h*(t - 2.5h)              para 2.5h ≤ t.                     (vuelta)

a)  ¿a qué distancia de la partida se encuentra con Bárbara?

Tenemos que ver cuando A(t) = B(t).

Para ello comparamos la vuelta de Agustín con la ida de Barbara.

7km -  5km/h*(t - 1.4h) = 3km/h*t  

7km - 5km/h*T + 7km = 3km/h*T

14km = 8km/h*t

14/8 h = 1.75h = t.

Entonces la posición en la que se encuentran es:

B(1.75h) = 3km/h*1.75h = 5.25km

Ellos se encuentran a 5.25 kilómetros de el punto de partida.

b)  Si en el momento del encuentro también Bárbara emprende el regreso

(Es decir, en este momento Barbara comienza a regresar).

Entonces ella para regresar al punto de inicio tiene que recorrer 5.25km con una velocidad de 3km/h.

Tb = 5.25km/3km/h = 1.75h

Barbara tarda 1.75 horas en regresar.

Agustín también tiene que recorrer 5.25 km para regresar, pero su velocidad es 5km/h.

Ta = 5.25km/5km/h = 1.05h.

La diferencia entre los tiempos es:

Tb - Ta  =1.75h - 1.05h = 0.7h

Entonces Barbara llega al punto de partida 0.7 horas después que Agustín.

Pero queremos esto en minutos.

1 hora = 60 minutos.

0.7 horas = 0.7*(60 min) = 42min

Barbara llega 42 minutos después que Agustín.


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