Question

three students, simone, jeffrey, and enzo, are washing cars for a fund - raiser. if all three students wash 1 car, it will take y minutes. if simone washes the car alone, it takes 40 minutes. if jeffrey washes the car alone, it takes 35 minutes. if it takes enzo x minutes to wash the car alone, which equation represents the amount of time it takes for the three students to wash the car?
\\(\frac{1}{y}=\frac{1}{40}+\frac{1}{35}+\frac{1}{x}\\)
\\(\frac{1}{y}=40 + 35 + x\\)
\\(y = \frac{1}{40}+\frac{1}{35}+x\\)
\\(y = 40 + 35 + x\\)

Explanation:

Step1: Define work rates

Work rate is $\frac{1}{\text{time to complete 1 task}}$.

• Simone's rate: $\frac{1}{40}$ cars per minute
• Jeffrey's rate: $\frac{1}{35}$ cars per minute
• Enzo's rate: $\frac{1}{x}$ cars per minute
• Combined rate: $\frac{1}{y}$ cars per minute

Step2: Sum individual rates

Combined rate = sum of individual rates.
$\frac{1}{y} = \frac{1}{40} + \frac{1}{35} + \frac{1}{x}$

Answer:

$\frac{1}{y} = \frac{1}{40} + \frac{1}{35} + \frac{1}{x}$