AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 25 Hard

On a certain bus route, there are 10 intermediate stops. There are two types of buses: express and local. The express bus travels at 1.2 times the speed of the local bus. The local bus stops at every station, while the express bus stops only at 1 intermediate station. The stop time at each station is 3 minutes. On one occasion, the local bus departs first. Forty minutes later, the express bus departs from the same starting station, and the two buses arrive at the terminal at the same time. How much time does the express bus take from the starting point to the terminal?

  • A.

    68

  • B.

    67

  • C.

    66

  • D.

    65

  • E.

    64

Answer:A

Let the distance from the starting point to the terminal be S, and let the speed of the local bus be 1.

The travel time for the local bus is S \div 1 = S \ \text{(minutes)}, and the total stopping time is 30 minutes.

From the problem statement: S + 30 - 40 = \frac{S}{1.2} + 3

which gives S = 78.

Therefore, the express bus takes 78 + 30 - 40 = 68 \ \text{minutes} from the starting point to the terminal.