micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. he rows back upstream…

micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. he rows back upstream the same distance, against the current, in 0.56 hours. assuming his rowing speed and the speed of the current are constant, what is the speed of the current?\n3 miles per hour\n8 miles per hour\n11 miles per hour\n14 miles per hour

micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. he rows back upstream the same distance, against the current, in 0.56 hours. assuming his rowing speed and the speed of the current are constant, what is the speed of the current?\n3 miles per hour\n8 miles per hour\n11 miles per hour\n14 miles per hour

Answer

Explanation:

Step1: Calcular la velocidad downstream

La velocidad $v_d$ cuando va downstream (con la corriente) se calcula usando la fórmula $v=\frac{d}{t}$. Aquí, $d = 4.48$ millas y $t = 0.32$ horas. Entonces $v_d=\frac{4.48}{0.32}=14$ millas por hora.

Step2: Calcular la velocidad upstream

La velocidad $v_u$ cuando va upstream (contra la corriente) se calcula usando la misma fórmula $v=\frac{d}{t}$. Aquí, $d = 4.48$ millas y $t = 0.56$ horas. Entonces $v_u=\frac{4.48}{0.56}=8$ millas por hora.

Step3: Encontrar la velocidad de la corriente

Sea $r$ la velocidad del remador y $c$ la velocidad de la corriente. Entonces $v_d=r + c$ y $v_u=r - c$. Sumando estas dos ecuaciones: $v_d+v_u=(r + c)+(r - c)=2r$. Restando: $v_d - v_u=(r + c)-(r - c)=2c$. Queremos $c$, y $c=\frac{v_d - v_u}{2}$. Sustituyendo $v_d = 14$ y $v_u = 8$, tenemos $c=\frac{14 - 8}{2}=3$ millas por hora.

Answer:

3 miles per hour