Bunuel wrote:
X and Y, two computer engineers, built identical websites at different constant rates. X, working alone for 7 hours, built some of the website; then Y, working alone for 6 hours, built the rest of the website. How many hours would it have taken X, working alone, to build all of the website?
(1) X built one part 15 minutes
(2) X built four times as many parts in 7 hours as Y built in 6 hours
Are You Up For the Challenge: 700 Level QuestionsLet the total work = 1 website
X worked alone for 7 hours and Y worked alone for 6 hours. Together they completed the 1 website.
If X normally takes (x) hours to complete the website: Efficiency of X = (1 website) / (x hours) = 1/x
if Y normally takes (y) hours to complete the website: Efficiency of Y = (1 website) / (y hours) = 1/y
(Efficiency) x (Time spent working) = Total work completed
(1/x) * (7 hours) + (1/y) * (6 hours) = 1 website
we want to know the time it would take X working alone, or:
what is the value of x = ?
s1: X built one part in 15 minutes
we do not know how many "parts" of which the website is made. Thus, there is no way to determine the amount of time it would take X, alone, to complete the entire website.
s1 not sufficient.
s2: X built 4 times as many parts in 7 hours as Y built in 6 hours
we are given: (1/x)(7) + (1/y)(6) = 1 website
No matter the size of the website, statement 2 tells us that X is 4 TIMES AS EFFICIENT as Y in the given times.
Since they were able to put together the entire computer in the given times, we can find the Ratio of work completed by each:
(Work done by X) : (Work done by Y) = 4 : 1
X: completed (4/5) of the website
Y: completed (1/5) of the website
so we know that X was able to complete (4/5) of the entire job in 7 hours.
7 hours
X ---------------------------> (4/5) of job
since Work and Time are directly proportional, the more work that has to be completed, the more time it will take:
7 hours (5/4)
X ------------------------------> (4/5) * (5/4) = 1 entire job
Time it would take X alone: (7) * (5/4) = 35/4 hours
s2 sufficient alone
*B*