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...

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?

Lian has traveled 1,000 kilometers when the two trains pass each other.

To find out how far Lian has traveled when the two trains pass each other, we can use the concept of relative speed. Since the trains are moving towards each other, their speeds will add up.

Let's denote:

• Yuto's speed as 220 km/h
• Lian's speed as 250 km/h

When two objects are moving towards each other, their relative speed is the sum of their individual speeds.

So, the relative speed of the two trains is 220 + 250 = 470 km/h.

The total distance between the two trains is 1,880 km.

We can use the formula:

Distance = Speed × Time

to find the time it takes for the two trains to meet.

Time = Distance / Speed

Time = 1,880 km / 470 km/h

Time = 4 hours

Since both Yuto and Lian have traveled for the same amount of time when they meet, we can calculate the distance Lian has traveled:

Distance = Speed × Time

Distance = 250 km/h × 4 hours

Distance = 1,000 km

So, Lian has traveled 1,000 kilometers when the two trains pass each other.

Distance. Time and Speed

Distance, time, and speed are interconnected concepts in physics and mathematics, often utilized to describe motion. Here's a breakdown of each:

1. Distance: Distance refers to the length of the path traveled by an object. It is a scalar quantity, meaning it has only magnitude and no direction. In most cases, distance is measured in units like meters (m), kilometers (km), miles (mi), etc.

2. Time: Time is the duration between two events or moments. It is also a scalar quantity, measured in units such as seconds (s), minutes (min), hours (hr), etc.

3. Speed: Speed is the rate at which an object covers distance. It's a scalar quantity as it only specifies how fast an object is moving, not the direction. Speed is calculated by dividing the distance traveled by the time taken. Mathematically, it's represented as:

   Speed = Distance / Time

   The units of speed depend on the units of distance and time used in the calculation. For example, if distance is measured in meters and time in seconds, then speed would be in meters per second (m/s). Similarly, if distance is in kilometers and time in hours, then speed would be in kilometers per hour (km/hr).

These concepts are fundamental to understanding motion and are widely used in various fields, including physics, engineering, and everyday activities.