Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?

Question

A table showing Rate in kilometers per hour, Time in hours, and Distance in kilometers. The first row shows, Yuto, and has 220, t, and 220 t. The second row shows, Lian, and has 250, t, and 250 t.

A. 470 kilometers
B. 880 kilometers
C. 940 kilometers
D. 1,000 kilometers

Answer 1

To find out how far Lian has traveled when the two trains pass each other, we can set up an equation using the information provided.

Let:

• \( t \) be the time in hours until they meet.
• Distance Yuto travels: \( 220t \) (since speed = 220 km/h).
• Distance Lian travels: \( 250t \) (since speed = 250 km/h).

The total distance between them is 1,880 kilometers. When the two trains meet, the distance covered by both trains will equal this total distance:

\[ 220t + 250t = 1880 \]

Combining the terms gives:

\[ 470t = 1880 \]

Now, solve for \( t \):

\[ t = \frac{1880}{470} \] \[ t = 4 \]

Now that we have the time when they meet, we can find out how far Lian has traveled:

\[ \text{Distance Lian traveled} = 250t = 250 \times 4 = 1000 \text{ kilometers} \]

Thus, the answer is:

D. 1,000 kilometers.