Question

supongamos que un satélite en órbita alrededor de la tierra recorre 50 kilómetros en 8 segundos. a esa tasa, ¿cuánto tiempo le tarda recorrer 250 kilómetros?
(a)
sea ( t ) la cantidad desconocida de tiempo que el satélite se tarda (en segundos). utiliza los valores siguientes para crear una proporción que sirva para encontrar ( t ).
valores:
( t ) ( 50 ) ( 8 ) ( 250 )
( \frac{square}{square} = \frac{square}{square} )
(b)
utiliza la proporción de la parte (a) para encontrar el tiempo que el satélite se tarda en recorrer 250 kilómetros. no redondees ningún cálculo.
segundos

Explanation:

Part (a)

Step1: Identify the proportion

The satellite's speed is constant, so distance and time are proportional. So we set up the proportion: $\frac{\text{Distance}_1}{\text{Time}_1}=\frac{\text{Distance}_2}{\text{Time}_2}$. Here, $\text{Distance}_1 = 50$ km, $\text{Time}_1 = 8$ s, $\text{Distance}_2=t$ (unknown time), $\text{Time}_2 = 250$? Wait, no, wait. Wait, the first part: Wait, the problem says "Supongamos que un satélite en órbita alrededor de la Tierra recorre 50 kilómetros en 8 segundos. A esa tasa, ¿cuánto tiempo le tarda recorrer 250 kilómetros?" Wait, maybe I misread. Wait, part (a) is to set up the proportion. So the known is 50 km in 8 s, and we need to find time $t$ for 250 km? Wait, no, the first part (a) is to create the proportion. So the proportion should be $\frac{t}{250}=\frac{8}{50}$? Wait, no, distance over time: $\frac{50}{8}=\frac{250}{t}$? Wait, no, let's clarify.

Wait, the satellite travels 50 km in 8 s. So the rate is 50 km per 8 s. We need to find the time $t$ it takes to travel 250 km. So the proportion is $\frac{\text{Distance}_1}{\text{Time}_1}=\frac{\text{Distance}_2}{\text{Time}_2}$. So $\frac{50}{8}=\frac{250}{t}$? Wait, no, if we are finding $t$ for 250 km, then $\frac{50}{8}=\frac{250}{t}$? Wait, no, maybe the other way. Wait, let's check the boxes. The boxes have $t$, 50, 8, 250. So the proportion is $\frac{t}{250}=\frac{8}{50}$? Wait, no, let's think: time over distance. If 50 km takes 8 s, then $t$ seconds for 250 km. So $\frac{8}{50}=\frac{t}{250}$. Yes, that makes sense. So the proportion is $\frac{8}{50}=\frac{t}{250}$.

Step2: Set up the proportion

So we place 8 (time for 50 km) over 50 (distance for 8 s) and $t$ (unknown time) over 250 (distance for $t$ s). So the proportion is $\frac{8}{50}=\frac{t}{250}$.

Part (b)

Step1: Solve the proportion

From the proportion $\frac{8}{50}=\frac{t}{250}$, we can cross - multiply. Cross - multiplying gives $50\times t = 8\times250$.

Step2: Calculate the right - hand side

Calculate $8\times250 = 2000$. So we have $50t=2000$.

Step3: Solve for $t$

Divide both sides by 50: $t=\frac{2000}{50}$.

Step4: Simplify

$\frac{2000}{50}=40$. So $t = 40$ seconds.

Answer:

(for part (b)):
The time the satellite takes to travel 250 kilometers is $\boxed{40}$ seconds.

(For part (a), the proportion is $\frac{8}{50}=\frac{t}{250}$ or $\frac{50}{8}=\frac{250}{t}$, but based on the boxes, it's likely $\frac{t}{250}=\frac{8}{50}$ or $\frac{8}{50}=\frac{t}{250}$)