Sumanta needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her

M7MBA wrote: ↑

Wed Oct 07, 2020 10:23 am

Sumanta 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 Sumanta 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

Answer: D

Solution:

Since the problem asks for the latest time she can begin typing and still meet the deadline of 5 pm, let’s check the answer choices in reverse order. That is, let’s begin with choice E (4:42 pm). Since 4:42 pm is 1 hour and 42 minutes, or 102 minutes, past 3 pm, and there are 102/2 = 51 two-minute intervals between 3 pm and 4:42 pm (inclusive), her speed is 20 + 51 = 71 wpm (words per minute) if she starts at 4:42 pm. Since she has 18 minutes until the deadline, she can type 71 x 18 = 1,278 words. However, this is fewer than the 1950 words she needs to type.

So let’s try choice D (4:30 pm) now. Since 4:30 pm is 1 hour and 30 minutes, or 90 minutes, past 3 pm, and there are 90/2 = 45 two-minute intervals between 3 pm and 4:30 pm (inclusive), her speed is 20 + 45 = 65 wpm if she starts at 4:30 pm. Since she has 30 minutes until the deadline, she can type 65 x 30 = 1,950 words. This is exactly the number of words she needs to type. So choice D is the correct answer.

Answer: D