# Problem of the Week Problem A and Solution Roller Coaster Riders

## Problem

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.

## Solution

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.