A certain printer can print at the rate of 80 characters per second

Question

A certain printer can print at the rate of 80 characters per second, and there is an average (arithmetic mean) of 2,400 characters per page. If the printer continued to print at this rate, how many minutes would it take to print an M-page report?

A. \(\frac{ M}{30}\)

B. \(\frac{M}{60}\)

C. \(\frac{M}{2}\)

D. \(\frac{2}{M}\)

E. \(\frac{60}{M}\)

A.  \frac{ M}{30}

B.  \frac{M}{60}

C.  \frac{M}{2}

D.  \frac{2}{M}

E.  \frac{60}{M}

philipssonicare · Answer

Rate (characters/second)=80
Rate (characters/minute)=4800

Work=2400·M

Time=Work/Rate
Time=2400M/4800=M/2

MarmikUpadhyay · Answer

Rate of printer = 80 characters per second. Characters per page = 2,400.
Minutes to print M-page report =?

M pages will have M * 2400 characters

Seconds required to print M * 2400 characters =  \frac{M * 2400}{80}  = 30M seconds
And, 30M seconds =  \frac{30M}{60}  minutes =  \frac{M}{2}  minutes.

So, correct answer is option  C .

argerniki · Answer

Let's Test it using some numbers: Let the report be 10 pages long --> M = 10 Therefore, the report has 10*2400 = 24000 pages \frac{24000}{80}=\frac{2400}{8}=300 seconds = 5 minutes Now let's plug in M = 10 and check the answers to see which option results in 5 minutes : A. \frac{M}{30}=\frac{10}{30} --> NO, too small (<1) B. \frac{M}{60}=\frac{10}{60} --> NO, too small (<1) C. \frac{M}{2}=\frac{10}{2}= 5 --> EXACTLY what we are looking for, but let's check D & E D. \frac{2}{M}=\frac{2}{10} --> NO, too small (<1) E. \frac{60}{M}=\frac{60}{10}= 6 --> NO, too big Therefore, Answer C

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A certain printer can print at the rate of 80 characters per second

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