Problem A and Solution

Roller Coaster Riders

A local amusement park has many roller coasters. On the roller coaster Gargantuan, the train has \(8\) cars, seating \(4\) guests in each car at one time. A ride starts every \(3\) minutes.

If the roller coaster was full every time, how many people rode the Gargantuan in a half an hour from the first ride starting? Justify your answer.

If there are \(8\) cars, and each car can hold \(4\) guests, then the maximum capacity of the roller coaster is \(8 \times 4 = 32\). In other words, at most \(32\) people can ride the Gargantuan at one time.

Half an hour is equal to \(30\) minutes. Now we can make a table to keep track of the total number of riders, if \(32\) people ride the Gargantuan every \(3\) minutes.

Time Elapsed
(minutes) |
Total Number of
Riders |
---|---|

\(3\) | \(32\) |

\(6\) | \(64\) |

\(9\) | \(96\) |

\(12\) | \(128\) |

\(15\) | \(160\) |

\(18\) | \(192\) |

\(21\) | \(224\) |

\(24\) | \(256\) |

\(27\) | \(288\) |

\(30\) | \(320\) |

Alternatively, we can calculate that in \(30\) minutes, there must be \(30 \div 3 = 10\) rides completed. Since the maximum capacity of one ride is \(32\) people, then the maximum number of riders in \(30\) minutes is \(32 \times 10 = 320\) people.