AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 17 Easy

The ratio of the speed of train A to that of train B was 5:4. Train B departed first and travelled from station B to station A. When it was 72\text{km} away from station B, train A left station A for station B. The two trains met each other at point X. The ratio of the distance between point X and station A to that between point X and station B was 3:4. The distance between station A and station B was （   ） \text{km}.

  • A.

    300

  • B.

    305

  • C.

    315

  • D.

    330

  • E.

    335

Answer:C

Let t be the time taken by A from departure until meeting B.

Let A’s speed be 5x, and B’s speed be 4x.

When A and B meet, the ratio of the distances they have traveled is \left( 72 + 4xt \right) : 5xt = 4 : 3, which simplifies to xt = 27.

Here, t is the time from A’s departure to the meeting.

Let the distance between A and B be s.

Then s = 72 + 4xt + 5xt = 72 + 9xt = 72 + 9 \times 27 = 315 \ \text{km}.

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