AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 19 Hard

At 8{:}37 in the morning, Yan leaves home on foot to go to school. Three minutes later, the dog starts running to chase him and catches up with him 200 meters from home. After catching up, the dog immediately runs back home, then immediately heads out again to chase Yan, catching him a second time 400 meters from home. After this second catch-up, the dog immediately runs back home again, then immediately heads out to chase Yan once more, and this time catches him exactly at the school. What time does Yan arrive at school?

  • A.

    8:57 a.m.

  • B.

    9:00 a.m.

  • C.

    8:55 a.m.

  • D.

    8:50 a.m.

  • E.

    8:40 a.m.

Answer:C

Yan's speed is \frac{200}{3} \times \frac{2}{3} = \frac{400}{9}.

The time from home to school is 400 \times 2 \div \frac{400}{9} = 18 \ \text{minutes}.

37 + 18 = 55.

Therefore, Yan arrives at school at 8{:}55.

Related Problems
Problem 17 AMC 8 Daily Practice Round 8
Problem 18 AMC 8 Daily Practice Round 8
Problem 20 AMC 8 Daily Practice Round 8
Problem 21 AMC 8 Daily Practice Round 8
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