Physics question about mechanics.....i need some help please!!?

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Two cyclists, A and B, have displacements 0 Km and 70 Km, respectively. At t = 0 they begin to cycle towards each other with velocities 15 Km/hr and 20 Km/hr, respectively. At the same time, a fly that was sitting on A starts flying towards B with a velocity of 30 Km/hr. As soon as the fly reaches B it immediately turns around and flies towards A, and so on until A and B meet.

a) What will the displacement of the two cyclists and the fly be when all three meet?

b) What will be the distance travelled by the fly?

(the answers in the back of the book are : a) 30 Km , b) 60 Km) (Can you please be very detailed with your answers and explain every step)
 
Are you SERIOUS?!? In what (textbook?) did you find this extraordinarily stupid (mathematical?) question?

To begin with, *displacements* are measured in cubic centimeters or cubic ft., etc.! And only speeds of objects are measured in Km/hr. etc.

Please! Go play with your "thing-ee" for further amusement!
 
First maybe you should draw a picture, something like:

A-->-------x--------<--B

This will help define our directions. So let's say that moving to the right is positive, moving to the left is negative. Therefore we can say that the cyclists are traveling:

A: v = +15 km/h
B: v = -20 km/h

We can write their positions as:

A: x = vo + v*t = 0 + 15t
B: x = vo + v*t = 70 - 20t

Where I've just used the (x = xo + vt + a*t*t/2 formula). You want to find out when they've reached the same point, ignore the fly here, since it will have to reach the same point as them at the same time since it's flying in between them. So you get:

A = B, or

0 + 15t = 70 - 20t, so

t = 2 hours

Now just throw that back into the position equations, but subtract the vo, since displacement 'd' is equal to:

d = x - xo

So you get:

A: x - xo = x = 15t
B: x - xo = x - 70 = - 20t

Sub in the value for 't' to get:

A: x - xo = 30 km
B: x - 70 = -40 km

So A was displaced 30km and B was displaced -40km or just 40km to the left.

The second part of this question is a bit of a trick. It really doesn't matter that the fly is going back and forth. It's always traveling 30km/hr. So if it took the two cyclists 2 hours to 'collide' and the fly was always traveling 30km/hr, the distance traveled was:

|d| = 30*t = 30*2 = 60km

I've put | | over the d in this case to distinguish between displacement and distance traveled. The fly's displacement is the same as cyclist A, but the distance traveled is 60km (I'm guessing you already know the difference between the two, so I won't bother explaining it).
 
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