Lolaergasheva wrote:

Machine A working alone can complete a job in hours. Machine B working alone can do the same job in hours. How long will it take both machines working together at their respective constant rates to complete the job?

(A) 1 hr 10 min

(B) 2 hr

(C) 4 hr 5 min

(D) 7 hr

(E) 8 hr 10 min

I got answer E but it is incorrect

PLEASE CHECK THE QUESTIONS WHEN POSTING.

Original question:

Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?

A. 1 hr 10 min

B. 2hr

C. 4hr 5 min

D. 7hr

E. 8 hr 10 min

General formula for multiple entities is \frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}, where

T is time needed for these entities to complete a given job working simultaneously.

For example if:

Time needed for A to complete the job is A hours;

Time needed for B to complete the job is B hours;

Time needed for C to complete the job is C hours;

...

Time needed for N to complete the job is N hours;

Then:

\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}, where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two entities A and B working simultaneously to complete one job:Given that

t_1 and

t_2 are the respective individual times needed for

A and

B (pumps, ...) to complete the job, then time needed for

A and

B working simultaneously to complete the job equals to

T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2} hours, which is reciprocal of the sum of their respective rates (

\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}).

For our original questions it'll be: 1/(7/2)+1/(14/3)=1/T --> T=2.

Answer: B.

Must know to solve work problems:

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