Rachel needs to type up her 1950-word paper by its 5 pm dead

BTGmoderatorDC wrote:Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

OA D

Source: Veritas Prep

Given that Rachel wishes to start by at least 2 hours before the deadline, she would have 2*60 = 120 minutes to type. Given that for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute, let's assume that she starts after n 2-minutes intervals, i.e. she starts type 2n minutes after 3 pm; thus, she types 1950 words in (120 – 2n) minutes. The speed at (120 – 2n) minutes before the finish of task would be (20 + n) words per minute.

Thus, the total number of words types = (120 – 2n)(20 + n) = 1950 => n = 45

Thus, Rachel can start by the latest (120 – 2n) = (120 – 2*45) = 120 – 90 = 30 minutes before 5 pm, or by 4:30 pm.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

OA D

Source: Veritas Prep

Let’s analyze the answer choices (in reverse order).

If Rachel starts at 4:42 pm (and notice that 4:42 pm is 102 minutes after 3 pm), she has to type 20 + 102/2 = 20 + 51 = 71 words per minute (wpm). Since she has only 18 minutes left until 5 pm, she can type 18 x 71 = 1278 words, which means she will miss the deadline of 5 pm. If Rachel starts at 4:30 pm (and notice that 4:30 pm is 90 minutes after 3 pm), she has to type 20 + 90/2 = 20 + 45 = 65 words per minute (wpm). Since she has only 30 minutes left until 5 pm, she can type 30 x 65 = 1950 words, which means she will just make the deadline of 5 pm.

Answer: D