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?

Time

(h)

Rate

(km/h)

220

250

Distance

(km)

220t

250t

Yuto

Lian

470 kilometers

880 kilometers

940 kilometers

1,000 kilometers

1,000 km

Step-by-step explanation:

Assume that when two train pass each other, Lian has traveled x (km)

=> The time Lian has traveled when two trains pass each other is:

Time = Distance / Rate = x / 250 (hour)

As Lian and Yuto travelled from the two opposite train stations and the train stations are 1,880 km apart

=> When two train pass each other, Yuto has traveled 1,880 - x (km)

=> The time Yuto has traveled when two trains pass each other is:

Time = Distance / Rate = (1,880 - x) / 220 (hour)

As Lian and Yuto board at the same time, so that when two trains pass each other, the time both of them have traveled is equal

=> x / 250 = (1,880 - x) / 220

=> 220x = 250 x (1,880 - x)

=> 220x = 470,000 - 250x

=> 470x = 470,000

=> x = 1,000

So that, when two train pass each other, Lian has traveled x = 1,000 km