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Hey CB34,
Good question - and kudos on seeking out additional rate problem practice!
Here's one example where the skills covered are GMAT-relevant but the numbers really aren't. The GMAT is great at picking numbers that allow for pretty convenient calculation if you perform the algebra well, and it's also great because it provides answer choices that you could use if the math ever gets cumbersome.
For the rate problem setup... When two people/machines are working together to complete a job, you can add the rates together, and that's a great step to take in this one.
Kristin's rate is 1 field / 11 hours, and Kayla's is 1 field / 16 hours. We can add those together:
1/11 + 1/16 = combined rate (in fields per hour)
What's ugly here is that there aren't any commonalities to the denominators so the math gets a little ugly:
1/11 = 16/176 and 1/16 = 11/176 (176 = 11*16, so that's your common denominator)
16/176 + 11/176 = 27/176
So your combined rate is 27/176, and we want to use that rate to solve for the amount of time it will take to harvest one field:
27/176 = 1 field / x hours
x(27/176) = 1
x = 176/27
Again, the GMAT would have answer choices here so you wouldn't have to do the long division. You could estimate this one to be near 180/30, which is 6, but the pure math breaks out to around 6.5.
NOW...the math is a little messy, and what's nice about GMAT problems is that the answer choices often save you from a lot of that. We know that, on her own, Kristin does 1 field in 11 hours. If we added one more Kristin, we'd just halve the time to 5.5. But Kayla is slower, so we need something a little longer than 5.5 hours to account for Kayla's slightly-slower speed. So if there were answer choices, you'd be looking for something around 6 or a little higher, and you might be able to get to 6.5-ish without actually doing the math...
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