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Work problem - Janice can mow the lawn . . .

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by Brent@GMATPrepNow » Tue Jan 27, 2009 3:15 pm
Janice can mow the lawn 50 minutes faster than it takes Rita to mow the same lawn. One day, after mowing the lawn by herself for 20 minutes, Janice quits. If it takes Rita 30 minutes to mow the remaining lawn, how many minutes would it take Janice to mow the entire lawn on her own?
(A) 20 sqrt2
(B) 10 sqrt10
(C) 4 sqrt70
(D) 15 sqrt5
(E) 16 sqrt5
Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.
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by sssudhak » Tue Jan 27, 2009 11:00 pm
Answer is B 10 sqrt 10.
Is that right?
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by chintudave » Tue Jan 27, 2009 11:52 pm
Let the time taken by J to mow the lawn is x.
Then, time taken by R is x + 50

In the first 20 minutes, the fraction of lawn mowed by J is 20/x

So fraction of lawn remaining for R is (1 - 20/x)

The time taken by R to mow the remaining lawn would be a product of
1. The fraction of lawn remaining
2. Time taken to mow the complete lawn.

i.e.
(1 - 20x)(x + 50) = 30
(x -20)(x + 50) = 30x
x2 + 30x - 1000 = 30x
x2 = 1000
x = 10 sqrt (10)

Hence B!
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by Brent@GMATPrepNow » Wed Jan 28, 2009 7:53 am
Nice work - the answer is B.
Here's my solution as well:

Let J = total number of minutes it takes Janice to mow the entire lawn
If Janice can mow the lawn 50 minutes faster than it takes Rita, we can conclude that it takes Rita J+50 minutes to mow the lawn

So, after 1 minute, the fraction of the lawn that Janice will have mowed is 1/J. After 20 minutes, the fraction of the lawn that Janice will have mowed is 20/J
Similarly, after 1 minute, the fraction of the lawn that Rita will have mowed is 1/(J+50). After 30 minutes, the fraction of the lawn that Rita will have mowed is 30/(J+50)

We can create the equation: fraction of lawn mowed by Janice + fraction of lawn mowed by Rita = 1
This means that 20/J + 30/(J+50) = 1
Multiply both sides by J(J+50) to get: 20J + 1000 + 30J = J^2 + 50J
Simplify to get: J^2 = 1000
This means J=sqrt(1000) =10sqrt10
Answer: B
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