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#1 2007-01-08 09:33:41

unique
Member
Registered: 2006-10-04
Posts: 419

emma could finish grading 10 papers in 20 minutes. grace could grade 15 papers in 25 minutes. if they worked together, how many minutes would it take emma and grace to grade 30 papers?

i did:

E = 10p in 20m
G = 15p in 25m

30 p in how many m

10p + 15p = 25p
20m + 25m = 45m

emma can grade 5p in 10m
so
10p + 15p + 5p = 30p
20m + 25m + 10m = 55m

Desi
Raat Key Rani !

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#2 2007-01-08 09:51:28

pi man
Member
Registered: 2006-07-06
Posts: 251

When you've completed a problem, always go back and compare your answer against the known facts and reason whether it could be correct or not.   Grace by herself can grand 15 papers in 25 minutes or 30 papers in 50 minutes.   Why why it take 5 minutes longer when both of them work together? (maybe they're sisters who fight a lot!)

Emma can grade 10 papers in 20 minutes = 1 paper in 2 minutes = 5 papers in 10 minutes.
Grace can grade 15 papers in 25 minutes = 3 papers in 5 minutes = 6 papers in 10 minutes.

Together they can grade 11 papers every 10 minutes.   That's less than 1 minute per test so you know your final answer will be less than 30 minutes.

30 tests / (11 tests / 10 minutes) = 30 tests * (10 minutes  / 11 tests) = 300 / 11 minutes = 27.2727... minutes.   Another helpful hint when doing these type of questions is to always include your units, which is "tests" and "minutes" in this case.    If your final answer doesn't work out to have "minutes" as the unit, you know you messed up somewhere.

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