Question 1034411
r*t = q
r = rate
t = time
q = quantity


first computer can grade 2000 exams in 10 seconds.
formula r*t = q becomes r*10 = 2000
solve for r to get r = 200
first computer can grade 200 papers per second.


when they work together their rates are additive.
formula becomes:
(200 + r)*3 = 2000
simplify to get 600 + 3r = 2000
subtract 600 from both sides to get 3r = 1400.
divide both sides by 3 to get r = 1400/3
second computer can grade 1400/3 papers per second.
that's equivalent to 466 and 2/3 papers per second.


working together, the formula becomes (200 + 1400/3) * 3 = 2000
simplify to get 2000 = 2000 which confirms the solution is correct.


when the new computer works alone, the formula becomes (1400/3) * t = 2000.
solve for t to get t = 2000 / (1400/3) = 2000 * 3/1400 = 6000/1400 seconds.
this is the same as 60/14 = 30/7 seconds.
in decimal format, that's equal to 4.285714286 seconds.
round that to 4.3 seconds.


it would take the new computer 4.3 seconds to do the grading on its own.