Two Trains and a Bee: Distance Question

[putongren]

Homework Statement

Two Trains and a Bee.
Consider two trains moving in opposite directions on the same track. The trains start simultaneouslyfrom two towns, Aville and Bville, separated by a distance d. Each train travels
toward each other with constant speed v. A bee is initially located in front of the train in
Aville. As the train departs Aville, the bee travels with speed u>v along the track towards
Bville. When it encounters the second train, it instantaneously reverses direction until it
encounters the first train, then it reverses again, etc. The bee continues flying between the
two trains until it is crushed between the trains impacting each other. The purpose of this
problem is to compute the total distance flown by the bee until it is crushed. Assume that
the bee is faster than the trains.

Relevant Equations

distance = rate * time

This is a question from the MIT Open courseware website.

(1). d = vt + ut let t = time it takes
d = (u + v)t
t = d / (u + v)
(2). d = vt + ut
d - vt = ut. Substitute t with d / (u + v)
d - v*(d/(u+v)) = u*(d/(u+v))
d - v*(d/(u+v)) = “distance of bee’s first flight"

This is to get the distance of the bee’s first flight. I’m not sure how to get the general equation for the nth flight, which is much harder. Does the general equation involve summation or series?

 

[Hill]

Homework Statement: Two Trains and a Bee.
Consider two trains moving in opposite directions on the same track. The trains start simultaneouslyfrom two towns, Aville and Bville, separated by a distance d. Each train travels
toward each other with constant speed v. A bee is initially located in front of the train in
Aville. As the train departs Aville, the bee travels with speed u>v along the track towards
Bville. When it encounters the second train, it instantaneously reverses direction until it
encounters the first train, then it reverses again, etc. The bee continues flying between the
two trains until it is crushed between the trains impacting each other. The purpose of this
problem is to compute the total distance flown by the bee until it is crushed. Assume that
the bee is faster than the trains.
Relevant Equations: distance = rate * time

Does the general equation involve summation or series?

No, it does not.

 

[haruspex]

Duplicate of https://www.physicsforums.com/threads/bees-and-trains-a-distance-problem.1063136/#post-7091776, yes?
Please do not post the same question twice.

 

[Mark44]

Thread locked. Any replies should go in the other thread -- https://www.physicsforums.com/threads/bees-and-trains-a-distance-problem.1063136/#post-7091776