Question

select the correct answer.
the time it takes to clean up after an anniversary party varies inversely as the number of people cleaning. if 3 people work together to clean, it will take them 90 minutes. how long will it take if the number of people cleaning is increased to 5?
a. 54 minutes
b. 72 minutes
c. 150 minutes
d. 162 minutes

Explanation:

Step1: Define inverse variation

Let \( t \) be time and \( n \) be number of people. Inverse variation: \( t=\frac{k}{n} \), so \( k = t\times n \).
For \( n = 3 \), \( t = 90 \), so \( k=90\times3 = 270 \).

Step2: Find time for \( n = 5 \)

Use \( t=\frac{k}{n} \), substitute \( k = 270 \), \( n = 5 \).
\( t=\frac{270}{5}=54 \)? Wait, no, wait. Wait, inverse variation: more people, less time. Wait, 3 people take 90 minutes. So total work is \( 3\times90 = 270 \) person - minutes. For 5 people, time \( t=\frac{270}{5}=54 \)? But wait, the options: A is 54. Wait, but let me check again. Wait, 3 people, 90 minutes: total work is \( 3\times90 = 270 \) units. If 5 people, time is \( 270\div5 = 54 \) minutes. So answer is A.

Answer:

A. 54 minutes