How much distance did the fly cover?

[insightful]

For the distance the fly flies, shouldn't you use the fly's velocity, v₃?

 

[Delta31415]

so v3=t*v1+v2

 

[insightful]

Back to basics. d=vt

 

[Delta31415]

d=vt
d=v3*d/(v1+v2)

 

[insightful]

d=vt
v3=d/(v1+v2)

Sorry, getting crossed messages.

Do you see that d, fly = v3*t?

 

[Delta31415]

yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

 

[insightful]

v3*d/(v1+v2)
equals
v3*d=v1+v2
right?

But we already know that t=d/(v1+v2).

We have the time the fly flies = t.
We have the velocity of the fly = v3.
We know d,fly = v3*t.

So what is d,fly in terms of the given variables: d, v1,v2, and v3?

 

[Delta31415]

i edited my meassge
so reposting it
yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

 

[insightful]

yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

Other than parentheses around the second v1+v2, my work here is done.

Please know that this puzzle has stumped many people (usually trying to solve it with an infinite series).

 

[Delta31415]

thank you for your help

 

[Delta31415]

Now i have a new problem, my teacher wants me to solve this using with infinite series? So how do infinite series work?