Question

jordan and james both work in a car wash. jordan can wash 3 cars in 30 minutes, and james can wash 5 cars in 60 minutes. at this rate, how many minutes will it take jordan and james to wash 22 cars? minutes =

Explanation:

Step1: Calculate Jordan's rate

Jordan can wash 3 cars in 30 minutes. His rate is $\frac{3}{30}=\frac{1}{10}$ cars per minute.

Step2: Calculate James's rate

James can wash 5 cars in 60 minutes. His rate is $\frac{5}{60}=\frac{1}{12}$ cars per minute.

Step3: Calculate combined rate

The combined rate of Jordan and James is $\frac{1}{10}+\frac{1}{12}$. First, find a common - denominator, which is 60. Then $\frac{1}{10}+\frac{1}{12}=\frac{6}{60}+\frac{5}{60}=\frac{6 + 5}{60}=\frac{11}{60}$ cars per minute.

Step4: Calculate time to wash 22 cars

Let $t$ be the time in minutes. We know that rate $\times$ time = work. So $t=\frac{22}{\frac{11}{60}}$. When dividing by a fraction, we multiply by its reciprocal: $t = 22\times\frac{60}{11}=120$ minutes.

Answer:

120