Solving an Algebra Problem with Trains and a Bird

[jojoba]

Two trains travel toward each other on the same track, beginning 100 miles apart. One train travels at 40 miles per hour; the other travels at 60 miles an hour. A bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. When it reaches the slower train, it turns around, flying the other direction at the same speed. When it reaches the faster train again, it turns around -- and so on. When the trains collide, how far will the bird have flown?
Bird
(Faster Train) A---------------------------------------B (Slower train)

My Attempt:
x: Time at which the two trains collide
100-40x=60x ====> x=1hr

x: Time at which the bird and train B collide

100-40x = 90x ====> x= 10/13 hr

90(10/13) - 90 ( 3/13) = 48 miles

The answer at the back of the book is 90miles. I don't understand what am I doing wrong. Could someone point me to my mistake?

 

[Dick]

The problem is asking you how far the bird is flying total, not just how far it flies until it meets train B for the first time. The trains collide in 1 hr. The bird is flying 90mi/hr during that whole period. So?

 

[jojoba]

I thought when they ask how far will the bird have flown is with respect to some origin, that's why I calculated the distance the bird had traveled when it hits Train B and subtracted the distance it travels in the opposite direction to the left in the remaining time which is 3/13 of an hour. but apparently I haven't understood the problem right. thanks