Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
Answers:	A) 3 and 1/3 weeks	B) 3 weeks	C) 2 and 1/2 weeks	D) 2 and 1/3 weeks	E) 2 weeks
VERITAS PREPOFFICIAL SOLUTION:   Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:   Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.   Rate (K) = 1 album / 5 weeks   Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.   Rate (C) = 1 album / x weeks   If the two emcees work together…   I’m adding these rates, so their combined rate is 1/5 + 1/x   …they can drop a full-length platinum compilation LP in 2 weeks.   And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2   Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?   I’m using that equation to solve for Common’s time, so I’m solving for x.   Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:   1/5 + 1/x = 1/2, so let’s get the x term on its own:   1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:   1/x = 5/10 – 2/10   1/x = 3/10, and from here you have options but let’s cross multiply:   10 = 3x, so divide both sides by 3 to get x alone:   10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice 3 and 1/3 weeks.
<result>A</result>
Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?