MathRevolution wrote:

Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

A. 12hrs B. 16hrs C. 24hrs D. 28hrs E. 32hrs

MvArrow , I got confused, too:

Machine A can do a job in 12 hours at a constant rate. Machine A

works for 4 hours. Machine B,

working at a constant rate, can do the same job at 2/3

the rate of machine A. If machine B does the rest

of the job, what is the amount of hours done by machine B alone?

Amount of work completed by Machine A?Work = 1 job

Rate of A:

\(\frac{1Job}{12hrs}=\frac{1}{12}\)Time that Machine A worked: 4 hours

Amount of work Machine A completes:

\(W = R * T\)

\(W = \frac{1}{12} * 4=\frac{4}{12}=\frac{1}{3}\) of Work finished

Work remaining for B:

\(\frac{2}{3}\)B's rate? B is slower than A

B's rate is

\(\frac{2}{3}\) the rate of (= multiply) A

B's rate:

\((\frac{1}{12}*\frac{2}{3})=\frac{2}{36}=\frac{1}{18}\) = rate of B

Time needed for B to finish work remaining?\(\frac{2}{3}\) of work remains

\(R * T= W\), so \(T = \frac{W}{R}\)Time for B:

\(\frac{\frac{2}{3}}{\frac{1}{18}}=(\frac{2}{3}*\frac{18}{1})=12\) hours

Answer A

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