Math Problem Statement

On a 165 km road segment AB, two people start traveling toward each other from points A and B. The speed ratio of the first person (from A) to the second person (from B) is 3:4. When they meet, the time ratio of the first person to the second person is 2:5. Calculate the distance each has traveled upon meeting.

Solution

This is a math problem written in Vietnamese. Let me break it down for you:

The problem is a time and speed problem, involving two people traveling along a road:

  • The distance from point A to point B is 165 km.
  • The two people leave points B and A, respectively, at the same time, but they travel at different speeds.
  • Their speeds have a ratio of 2:3.
  • After traveling for a certain amount of time, they meet. The time it takes for them to meet is also given in a ratio, 2:5.
  • The goal is to find the distance each person has traveled when they meet.

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Math Problem Analysis

Mathematical Concepts

Speed, Distance, and Time
Ratios and Proportions
Linear Equations

Formulas

Distance = Speed × Time
Ratio properties
Time = Distance / Speed

Theorems

Ratio and Proportion Theorem
Distance-Speed-Time Relationship

Suitable Grade Level

Grades 8-10

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