Question

Two trains start from Fort Worth traveling at the same speed. The trip for Train W takes 20 hours, while the trip for Train Z takes 25 hours. If the city Train Z is traveling to is 400 miles farther away than the city Train W is traveling to, how far will each train travel in total to reach its destination?
Which of the following rational equations best models this situation?

a. x/25 = x+400/20

b. x/20 = x+400/25

c. x/20 = x/25 - 400

d. x/20 = x-400/25

e. x/20 + 400 = x/25

Answer 1

Answer:

The equation that best models this situation is :

b. $\frac{x}{20}=\frac{x+400}{25}$

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 = $x$ miles

Speed of Train W can be given as :

⇒ $\frac{Distance}{Time}$

⇒ $\frac{x}{20}\ miles/h$

So, the length of the trip of Train Z will be = $(x+400)$ miles

Speed of Train Z can be given as :

⇒ $\frac{Distance}{Time}$

⇒ $\frac{x+400}{25}\ miles/h$

Since the speeds are same, so the equation to find $x$ can be given as:

⇒ $\frac{x}{20}=\frac{x+400}{25}$

Solving for $x$

Multiplying both sides by 100 to remove fractions.

⇒ $100\times \frac{x}{20}=100\times \frac{x+400}{25}$

⇒ $5x=4(x+400)$

Using distribution.

⇒ $5x=4x+1600$

Subtracting both sides by $4x$

⇒ $5x-4x=4x-4x+1600$

⇒ $x=1600$

Thus, Distance traveled by Train W = 1600 miles

Distance traveled by Train Z = $1600+400$ = 2,000 miles