Question

Juan camina a 2km/h del punto A a B y regresa trotando a 3km/h. si en total demora 10 h en ir y volver. Calcula la distancia AB.

Answer 1

Datos:

$v_{_{AB}} = 2\frac{km}{h} \\ v_{_{BA}} = 3\frac{km}{h} \\ t = 10h \\ d_{_{AB}} = ?$

Desarrollo:

$v_{_{AB}} = \frac{d}{t_{1}} \\ d = v_{_{AB}} * t_{1} \\\\ v_{_{BA}} = \frac{d}{t_{2}} \\ d = v_{_{BA}} * t_{2} \\\\ t_{1} + t_{2} = 10 \\ t_{1} = 10 - t_{2}$

$v_{_{AB}} * t_{1} = v_{_{BA}} * t_{2} \\ v_{_{AB}} * (10 - t_{2}) = v_{_{BA}} * t_{2} \\ 2(10-t_{2}) = 3t_{2} \\ 20 - 2t_{2} = 3t_{2} \\ 5t_{2} = 20 \\ t_{2} = 4h$

$d = v_{_{BA}} * t_{2} \\ d = 3*4 \\d = 12km$

Respuesta:

La distancia de AB es de 12km