Question

A boat traveled 210 miles downstream and back. The Trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
Hint: The downstream equation is 10(b + c)= 210 because distance = rate*time


Doy 40 puntos, muchas gracias

Answer 1

A boat traveled 210 miles downstream and back. The Trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current? 
Hint: The downstream equation is 10(b + c)= 210 because distance = rate*time

La ecuación agua arriba es:
70 (b - c) = 210

La ecuación gua abajo es:
10 (b + c) = 210

Aplicamos propiedad distributiva en ambas ecuación.
1) 70b - 70c = 210
2) 10b + 10c = 210

Resolvemos por el MÉTODO de IGUALACIÓN.
-Despejamos "b" en las dos ecuaciones.
70b - 70c = 210              10b + 10c = 210
70b = 210 + 70c             10b = 210 - 10c
b = (210 + 70c)/70           b = (210 - 10c)/10

Igualamos las dos ecuaciones.
(210 + 70c)/70 = (210 - 10c)/10

Multiplicamos en cruz, las ecuaciones.
10 (210 + 70c) = 70 (210 - 10c)
2100 + 700c = 14700 - 700c
700c + 700c = 14700 - 2100
1400c = 12600
c = 12600/1400
c = 9

El valor de "c" lo reemplazamos en uno de los despeje de "b".
b = (210 - 10c)/10
b = (210 - 10 (9))/10
b = (210 - 90)/10
b = 120/10
b = 12

RESPUESTA:
-La velocidad del bote = 12 mi/h
-La velocidad de la corriente es = 9 mi/h