Respuesta :
Answer:
The equation that best models this situation is :
b. [tex]\frac{x}{20}=\frac{x+400}{25}[/tex]
Distance traveled by Train W = 1600 miles
Distance traveled by Train Z = 2,000 miles
Step-by-step explanation:
Given:
Time taken for Train W to complete a trip = 20 hours
Time taken for Train Z to complete a trip = 25 hours
The city Train Z is traveling to is 400 miles farther away than the city Train W is traveling to.
both trains have same speeds and start from same location.
To find the distance in total each train travels.
Solution:
Let length of the trip of Train W be = [tex]x[/tex] miles
Speed of Train W can be given as :
⇒ [tex]\frac{Distance}{Time}[/tex]
⇒ [tex]\frac{x}{20}\ miles/h[/tex]
So, the length of the trip of Train Z will be = [tex](x+400)[/tex] miles
Speed of Train Z can be given as :
⇒ [tex]\frac{Distance}{Time}[/tex]
⇒ [tex]\frac{x+400}{25}\ miles/h[/tex]
Since the speeds are same, so the equation to find [tex]x[/tex] can be given as:
⇒ [tex]\frac{x}{20}=\frac{x+400}{25}[/tex]
Solving for [tex]x[/tex]
Multiplying both sides by 100 to remove fractions.
⇒ [tex]100\times \frac{x}{20}=100\times \frac{x+400}{25}[/tex]
⇒ [tex]5x=4(x+400)[/tex]
Using distribution.
⇒ [tex]5x=4x+1600[/tex]
Subtracting both sides by [tex]4x[/tex]
⇒ [tex]5x-4x=4x-4x+1600[/tex]
⇒ [tex]x=1600[/tex]
Thus, Distance traveled by Train W = 1600 miles
Distance traveled by Train Z = [tex]1600+400[/tex] = 2,000 miles
The following rational equations best model this situation is;
[tex]\rm \dfrac{x}{20}= \dfrac{x+400}{25}\\\\[/tex], the correct option is B.
The distance covered by each train travel in total to reach its destination is 2000 miles.
The distance covered train W is 1600.
Given
Time is taken for Train W to complete a trip = 20 hours
Time is taken for Train Z to complete a trip = 25 hours
What is the relation between distance and speed?
The relation between distance and speed is given by;
[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]
Let, the length of the trip of Train W be x.
The length of the trip of Train Z is (x+400).
Then,
The Speed of Train W is given by;
[tex]\rm Speed \ W = \dfrac{Distance}{Time}\\\\ Speed \ W = \dfrac{x}{20}[/tex]
And Speed of Train Z is given by;
[tex]\rm Speed \ Z = \dfrac{Distance}{Time}\\\\ Speed \ Z = \dfrac{x+400}{25}[/tex]
Therefore,
The following rational equations best model this situation is;
[tex]\rm \dfrac{x}{20}= \dfrac{x+400}{25}\\\\25x=20(x+400)\\\\ 25x=20x+8000\\\\25x-20x=8000\\\\5x=8000\\\\x=\dfrac{8000}{5}\\\\x=1600[/tex]
The distance covered train W is 1600.
The distance covered by each train travel in total to reach its destination is;
= 1600 + 400 =2000 miles
Hence, the distance covered by each train travel in total to reach its destination is 2000 miles.
To know more about speed distance click the link given below.
https://brainly.com/question/17099429
