# A Ferris wheel can accommodate 70 people in 20 minutes. How many people could ride the Ferris...

## Question:

A Ferris wheel can accommodate 70 people in 20 minutes. How many people could ride the Ferris wheel in 4 hours?

## Applications of Proportions:

In mathematics, a proportion is an equation of the form {eq}\frac{a}{b}=\frac{c}{d} {/eq} that indicates that the two ratios, a : b and c : d, are equivalent. We can set up a proportion representing various applications involving ratios, and then use that proportion to find any missing or unknown values in the problem.

If a Ferris wheel can accommodate 70 people in 20 minutes, then the ratio comparing the amount of people the Ferris wheel can accommodate to the number of minutes it can do this in is given by {eq}\frac{70\; people}{20\; minutes} {/eq}. Simplifying this ratio gives that the Ferris wheel can accomodate {eq}\frac{7\; people}{2\; minutes} {/eq}, or 7 people every 2 minutes.

We want to know how many people the Ferris wheel can accomodate in 4 hours, so let's let this number be x. Since our ratio gives how many people in minutes for the Ferris wheel, we need to convert 4 hours to minutes. There are 60 minutes in one hour, so in 4 hours, there are 60 × 4 minutes, or 240 minutes. Thus, the ratio comparing the number of people the Ferris wheel can accomodate in 4 hours to the number of minutes it can do this in is given by {eq}\frac{x\; people}{240\; minutes} {/eq}. This ratio is equivalent to the ratio {eq}\frac{7\; people}{2\; minutes} {/eq}, because it is the same Ferris wheel. Therefore, we have the following proportion.

• {eq}\displaystyle \frac{x}{240}=\frac{7}{2} {/eq}

We can solve this for x to determine the number of people the Ferris wheel can ride in 4 hours. First we multiply both sides of the equation by 240 and by 2 to eliminate the fractions.

• {eq}2x=7\cdot 240 {/eq}

Simplify the right-hand side.

• {eq}2x=1680 {/eq}

Divide both sides by 2.

• {eq}x=840 {/eq}

We get that x = 840, so the Ferris wheel can ride 840 people in 4 hours.