Bunuel wrote:
A certain business printer can print 40 characters per second, which is 4 times as fast as an average printer. If an average printer can print 5 times as fast as an electric typewriter, how many characters per minute can an electric typewriter print?
(A) 2
(B) 32
(C) 50
(D) 120
(E) 600
ShortcutFind the first rate in minutes.
"Certain" business printer's rate in characters, \(c\), per 1 minute:
\(\frac{40c}{1sec}*\frac{60}{60}=\frac{2,400c}{60secs}=\frac{2,400c}{1 minute}\)
Shortcut:
All rates are per 1 minute
Let the different machines be B, AP, and ET
Rate of B is 5 times as fast as that of AP
Rate of AP is 4 times as fast as that of ET
Hence B's rate is (5*4) = 20 times as fast as ET's rate
\(2,400c=20*ET\)
\(ET=\frac{2,400c}{20}=120c\)
\(ET=\frac{120c}{1 min}\)
In one minute, the electric typewriter can type 120 characters
Answer D
In steps"Certain" business printer's rate from above:
\(\frac{2,400c}{1 minute}\)
That rate is 4 times as fast as the average printer's rate, AP:
\(2,400c=(4*AP)\)
\(AP=\frac{2,400c}{4}=600c\)
\(AP=\frac{600c}{1 min}\) THAT per minute rate, AP, is 5 times as fast as an electric typewriter's per minute rate, ET:
\(600c=5*ET\)
\(ET=\frac{600c}{5}=120c\)
Electric typewriter rate: \(\frac{120c}{1min}\)In one minute, the electric typewriter can type 120 characters
Answer D
*All rates based on a prior PER MINUTE rate are also per minute _________________
Any fool can know. The point is to understand. — Albert Einstein