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Possible Error GMAT Review 12th edition

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Possible Error GMAT Review 12th edition [#permalink] New post 03 Jun 2010, 21:05
Someone please show me the error of my ways if I am incorrect...

Question 149 on page 173 of the Official Guide for GMAT Review 12th Edition:
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

Here is what I did:
Total Time = Time at 40mph + time at 60mph (Time= Distance/Rate)
Total Distance = d
Total Time = xd/40 + [(100-x)d]/60
make 120 common denominator and distribute the d
Total Time = 3xd/120 + [200d-2xd]/120
add fractions
Total Time = [xd+200d]/120
factor out d
Total Time = d(x+200)/120
Average Speed = total distance/total time
Average speed = d/[d(x+200)/120]
dividing by a fraction is the same as multiplying by the recipricol
Average Speed = d * 120/d(x+200)
the distance cancels
Average speed = 120/(x+200) MY ANSWER
BOOK ANSWER 12,000/x+200

I think the book is wrong because they assume in the problem that her trip is 100 miles, but if they do that, then they need to divide out the 100 assumed miles at the end

Can someone please let me know if there is something incorrect in my work, or if the book is wrong

Thanks :)
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Re: Possible Error GMAT Review 12th edition [#permalink] New post 03 Jun 2010, 22:43
I think u r wrong...

Q says : Francine traveled x percent of the total distance

Therefore : xd/40 should be x% of d i.e. x/100 * d * 1/40
Similar way the second part of the equation should also be divided by 100...

So complete equation would be divided by 100 which would change the denominator of Total Time = [xd+200d]/120 from 120 to 12000...

Finally the ans would be BOOK ANSWER 12,000/x+200..

Hope its clear..
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Re: Possible Error GMAT Review 12th edition [#permalink] New post 04 Jun 2010, 08:10
That makes sense. Thanks for your help, it is much appreciated! :-D
Re: Possible Error GMAT Review 12th edition   [#permalink] 04 Jun 2010, 08:10
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