Bunuel wrote:

At an auto detailing company, it takes 15 minutes for an employee to service a car and 24 minutes to service a truck. If the company needs to service all 300 trucks and 360 cars on a lot during a six-hour shift, how many employees will it need to complete the job?

A. 35

B. 36

C. 40

D. 42

E. 45

Attachment:

#rtwtable.png [ 29.05 KiB | Viewed 394 times ]
Careful . . . prompt lists "cars and trucks,"

then "trucks and cars"

We have rate in minutes, time in hours, and total W

Find rate in hours. With R, T, and W, find # of employees.

(1) Find RATE in # of vehicles/HOUR

Cars: 15 minutes each

Rate,

\(R\): How many cars per hour?

\(R_{c}:\) \(\frac{1}{15min}=\frac{4}{60min}=\)

\(R_{c}:\) \(\frac{4}{1hr}\)\(=4\) cars per hour

Trucks: 24 minutes each

Rate,

\(R\): How many trucks per hour?

\(R_{t}:\) \(\frac{1}{24}=\frac{2.5}{60}\)

\(=\frac{\frac{5}{2}}{60min}=\frac{\frac{5}{2}}{1hour}\)

\(R_{t}\): \(=\frac{5}{2}\) cars per hour

(2) How many employees needed to complete the job?

Use modified RT=W equation (see table)

Cars: # of workers needed to finish 360 in 6 hours?

(Number, N, of workers) * R * T = W\(N_1 * 4 * 6 = 360\)

\(N_1 = \frac{360}{24}\)

\(N_1 = 15\)Trucks: # of workers needed to finish 300 in 6 hours?

(N) * R * T = W\(N_2 * \frac{5}{2} * 6 = 300\)

\(N_2 * \frac{30}{2} = 300\)

\(N_2 * 15 = 300\)

\(N_2 = 20\)

(3) Total workers/employees needed:

\((15 + 20) = 35\)Answer A
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