Abby and Bobby type at constant rates of 80 words per minute

AAPL wrote:Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?

A. 1:40 PM
B. 1:50 PM
C. 2:00 PM
D. 2:10 PM
E. 2:20 PM

We can create the equation:

Time = (change in work)/(change in rate)

We see that the change in rate is 80 - 60 = 20. However, the change in work is not 200. That is because Bobby has a head start of 600 words before Abby even begins typing. So when Abby has typed exactly 200 more words than Bobby, she actually needs to type 600 + 200 = 800 more words than Bobby at the time she begins typing at 1:30 pm.

Time = 800/20 = 40 minutes

So at 2:10 pm she has typed 200 more words than Bobby.

Alternate Solution:

Abby types 20 words more than Bobby for each minute. When Abby begins typing at 1:30, Bobby has already typed 600 words. So she will need to type 600/20 = 30 minutes just to catch up to Bobby. We want to know how long it will take her to type exactly 200 words more than Bobby, so from the point in time that she caught up to him, she will need an additional 200/20 = 10 minutes. Thus, the total time she needs to type is 30 + 10 = 40 minutes. She began to type at 1:30 pm, so at 2:10 pm, she will have typed 200 more words than Bobby.

Answer: D