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 ANSWERBOOK ANSWER 12,000/x+200I 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