AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 21 Medium

After its speed was increased, a certain train departed from City A at 21{:}00 and arrived punctually at City B at 07{:}00 the next day. Its travel time was 2 hours shorter than before the speed increase, and its average speed was 20~\text{km/h} faster than before. What is the distance between the two cities (in \text{km})?

  • A.

    800

  • B.

    1000

  • C.

    1200

  • D.

    1400

  • E.

    1500

Answer:C

Let the train’s speed before the increase be v km/h, and the distance between the two cities be s~\text{km}.

From the problem, the following equations can be set up:

\begin{cases}\frac{s}{10} = v + 20 \\[4pt]\frac{s}{12} = v\end{cases}

It is easy to solve and obtain v = 100, s = 1200.

Related Problems
Problem 19 AMC 10 Weekly Practice Round 2
Problem 20 AMC 10 Weekly Practice Round 2
Problem 22 AMC 10 Weekly Practice Round 2
Problem 23 AMC 10 Weekly Practice Round 2
Think Academy Powered by ChatGPT