Aki: 80 wpm
Brune: 60 wpm
Brune starts first and types 600 words before Aki starts at 1:30 pm. The question asks how long it will take before Aki will have typed exactly 200 more words than Brune.
It's possible to write equations to solve this kind of problem...but why bother? Just sketch it out, step by step. The answer choices are in 10 min increments, so check each answer, in order, till you find the one that works.
Every 10 minutes, Brune types 600 words and Aki types 800 words.
Find the time at which Aki is 200 more than Brune.
At 1:30 pm: B = 600 words, A = 0 words
(A) 1:40 pm: B = 1,200 words, A = 800 words...Brune is ahead. Eliminate.
(B) 1:50 pm: B = 1,800 words, A = 1,600 words...Brune is still ahead. Eliminate.
(C) 2:00 pm: B = 2,400 words, A = 2,400 words...They're equal. Eliminate.
Glance at the pattern. Notice anything?
Aki is catching up by 200 words every 10 minutes. At 2 pm, they're even, so 10 minutes later, Aki should be 200 words ahead of Brune. If you're not sure, check the math.
(D) 2:10 pm: B = 3,000 words, A = 3,200 words...Yep, Aki is 200 ahead of Brune.
The correct answer is (D).
Tip: Whenever you're sketching out a rate problem in the way shown above, if the people (or trains or whatever) are traveling at constant rates, then there will always be a pattern. It's very rare for the GMAT to have a rate problem in which the rate is not constant. So use that knowledge to your advantage when you're solving: Look for a pattern. In the above case, you can find the pattern after calculating answers (A) and (B) and then solve more quickly from there:
(A) 1:40 pm: B = 1,200 words, A = 800 words...Brune is 400 ahead. Eliminate.
(B) 1:50 pm: B = 1,800 words, A = 1,600 words...Brune is 200 ahead. Eliminate.
(C) 2:00 pm: Aki is catching up by 200 words every 10 minutes, so they'll be even here.
(D) 2:10 pm: Aki will be 200 ahead of Brune here.
