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 Train Z travel in total to reach its destination?

a) 1,200 miles
b) 480 miles
c) 2,400 miles
d) 2,000 miles
e) 1,600 miles

Answer 1

The equation that best models this situation is : b.

Distance traveled by Train W = 1600 miles

Distance traveled by Train Z = 2,000 miles

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 = miles

Speed of Train W can be given as :

⇒

⇒

So, the length of the trip of Train Z will be = miles

Speed of Train Z can be given as :

⇒

⇒

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

⇒

Solving for

Multiplying both sides by 100 to remove fractions.

⇒

⇒

Using distribution.

⇒

Subtracting both sides by

⇒

⇒

Thus, Distance traveled by Train W = 1600 miles

Distance traveled by Train Z = = 2,000 miles