Q:

Neil and Yuki run a data entry service. Neil starts at 9:00am and can type 45 words per minute. Yuki arrives at 10:30am and can type 60 words per minute. Write and solve an inequality to find at what time Yuki will have typed more words than Neil. Let x represent the time in minutes.

Accepted Solution

A:
Answer:270mStep-by-step explanation: Lets define two functions that describe Neil and Yuri productivity, depending on the hours.As Neil starts at 9 and types 45 words per minute (wpm), he will have typed the following words at the respective hours:at 9:30 -> 45 * 30 (as he have worked 30 minutes typing 45 wpm)at 10:00 -> 45 * 60at 10:30 -> 45 * 90 = 4,050at 11:00 -> 45 * 120 and so on.The same we can do for Yuki:at 11:00 -> 60* 30at 12:00 -> 60*60and so on.Let X be any time of the day measured in minutes after 10:30, which is the minimun time we can consider (our answer wont be a time beofre 10:30 as Yuki will have 0 words typed). This is, if X=20, the hour is 10:30 plus 20 minutes, it is, 10:50. We need to measure this way as its difficult to work with the sexgesimal system.So, now we can define the wpm production of both Neil and Yuki as a function of the time worked. Lets call Neil production N(X) and it will be equal to the words typed at 10:30 plus the extra words by minute:N(X) =  4050 + 45XThe same for Yuki. Y(X) is the words typed at 10:30 plus his production per minute:Y(X) = 0 + 60X = 60XNow we need Yuki to tyoe more words than Neil, it is, Y(X) > N(X):60X > 4050 + 45XLets subtract 45X in both sides to leave Xs all at one side:60X - 45X > 4050 + 45X - 45X15X > 4050Dividing both sides by 15:X > 4050/15X > 270So, after 270 minutes Yuki will hace typed more than Neil.