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About 1-3 miles[^].
And I won't comment the speed.
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It doesn't say the mosquito is flying under its own power, merely that it's travelling. Clearly it's hitched a lift.
I am not a number. I am a ... no, wait!
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What you didn't mention is that the mosquito is actually an omni-present alien space mosquito spanning galaxies in size.
Only the mighty mosquito knows the answer...
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Bassam Abdul-Baki wrote: How far will the mosquito travel?
It depends on the size of the mosquito; if it's bigger than the bikes, I suggest investigating an emergency fallback position.
You always obtain more by being rather polite and armed than polite only.
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time to meet faster = 2,8571428571428571428571428571429 hours
slower travel = 28,571428571428571428571428571429 miles
faster travel = 42,857142857142857142857142857143 miles
sum = 71,428571428571428571428571428572 miles
100 - 71,428571428571428571428571428572 = 28,571428571428571428571428571428 miles left to travel for mosq
time to meet slower = 0,95238095238095238095238095238093 hours
sum time mosq = 3,8095238095238095238095238095238 hours
total travell = 76,190476190476190476190476190477 miles = 76,2 miles
Edit 1:
Well, i didn't notice that it will "continuing to go back and forth", so the hard way is to find a sum limit for the infinite converging series, and the easy way is just 100/25*20 = 80, assuming the mosq have no inertia.
Edit 2: solving the hard way
time 0 = 2,8571428571428571428571428571429 h
time 1 = 0,95238095238095238095238095238093 h
time 2 = 0,95238095238095238095238095238093 * k h,
where k = 0,95238095238095238095238095238093 / 2,8571428571428571428571428571429 = 0,333(3)
time 2 = 0,3174603174603174603174603174603
time N = (0,333)^N * time0
https://upload.wikimedia.org/math/0/a/9/0a9e133cbd05d4d17f9f98b65765bb5a.png[^]
Sum [t0 * (0,333)^N] = t0 / (1 - 0,333) = 3,677146534289391432248575105718 h
well, thats only 73,543 miles, not 80
modified 27-May-16 10:07am.
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Easy way is easy... 80 miles (It's obviously a robotic mosquito)... Hard way is more interesting... And distracts me from the air conditioner that's trying to freeze me to my desk.
I wrote a solver (If you could call it that) in Excel...
s = Position of slow bike (Starts at 0, increases)
f = Position of fast bike (Starts a 100, decreases)
Trip 1:
Time = (f - s) / (20 + 15) = 2.8571429
s = 28.57143, f = 57.14286
Distance Traveled = 57.14286
Trip 2:
Time = (f - s) / (20 + 10) = 0.952381
Total Time = 3.809524
s = 38.09524, f = 42.85714
Distance Traveled = 76.19048
Trip 3:
Time = (f - s) / (20 + 15) = 0.1360544
Total Time = 3.945578
s = 39.45578, f = 40.81633
Distance Traveled = 78.91156
Trip 4:
Time = (f - s) / (20 + 10) = 0.0453515
Total Time = 3.99093
s = 39.9093, f = 40.13605
Distance Traveled = 79.81859
Trip 5:
Time = (f - s) / (20 + 15) = 0.0064788
Total Time = 3.997408
s = 39.97408, f = 40.03887
Distance Traveled = 79.94817
And so on... Next iteration it hits 79.99136, then 79.99753... Excel starts rounding to "80" on the 12th iteration.
By the end, the mosquito is just vibrating between the bikes... It would oscillate faster and faster, which would of course start to generate heat. Thermodynamics, right? Since this converges over infinity, the vibrations will just increase infinitely, which means more and more energy... And eventually it would turn into a miniature star, then a singularity, and then all of space/time would collapse.
Either that, or it would just get squished between the tires.
(Channeling my inner Randall... He must have done this in 'What If' by now...)
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I was trying to get a pattern for the infinite sequence. Pain in the patootie.
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I would think the twist is the distance keeps reducing, a normal calculation would not work.
First claculate where the Mos and the fast bike meet.
next calculat how far the slow bike travled.
subtract those from 100 that would be the next distance travled.
Next calculate from where fast bike and mos met to the where the slow bike will meet.
next claculate how far the Fast bike travled while mos was heading to meet the slow bike.
subtract those from the last number for distance.
you would have to keep going back and forth till the bikes met and the distance is zero.
Would it come out the same as a formula listed ?
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To C or not to C
That is the question
... such stuff as dreams are made on
And our little lives are rounded
With a curly brace
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To C sharper or not, is another question.
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Should have gone to Specsavers
That is the answer. 
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
- Homer
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R not Julia the Ruby of the realm?
Go hither and think not upon Ada,
Whose Basic baseness is not worthy a Boo,
C to it sharply and bring Clojure Forth,
Dart away now to her awaiting arms,
As her love for you awaits in the Eiffel tower of her heart,
Like an Elixir to her suffering,
Be not a Hack, a Python in the weeds, but be instead Groovy,
Woo her with Java,
Be Lithe, speak Lucid and without a Lisp,
Utter not a bovine Moo from thy lips,
Instead may an Opal be upon thy tongue,
Your Prolog Swift,
Your Smalltalk small,
Scheme little, for honesty is the Unicorn
upon which no Rust will form.
Marc
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Not impressed, you didn't fit JavaScript in there! 
- I would love to change the world, but they won’t give me the source code.
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Methinks Hamlet would've preferred:
"To B[^] or not to B[^]...
That is the question."
/ravi
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C programmers would've preferred:
int the_question = (2*b) | !(2*b);
GOTOs are a bit like wire coat hangers: they tend to breed in the darkness, such that where there once were few, eventually there are many, and the program's architecture collapses beneath them. (Fran Poretto)
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I'm about to kick off a new project in C#. There is no legacy to worry about and so I'm thinking what environment to use.
I shall shortly install Visual Studio, it is up to you, dear Cpians, to distruct in which version* to go for....
* I would love to go back to the simplicity of VS6 but those days are gone 
veni bibi saltavi
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VB3 - those were good times... 
Anything that is unrelated to elephants is irrelephant
Anonymous
-
The problem with quotes on the internet is that you can never tell if they're genuine
Winston Churchill, 1944
-
I'd just like a chance to prove that money can't make me happy.
Me, all the time
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I can, hand on heart, say I really liked VB6. I wouldn't go near it today, but at the time I liked it. VB3 has a frogging script and UI engine but it got us some good sales.
veni bibi saltavi
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I liked VB6 too. VB3 was my first IDE; and I like it for that, but seriously, the IDE itself wasn't very good. Free floating windows à la Delphi where you can see the desktop behind it and get distracted by that wasn't really my thing...
Anything that is unrelated to elephants is irrelephant
Anonymous
-
The problem with quotes on the internet is that you can never tell if they're genuine
Winston Churchill, 1944
-
I'd just like a chance to prove that money can't make me happy.
Me, all the time
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I even, briefly, thought about having a play VB.net. But then I sobered up.
veni bibi saltavi
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What kind of project is it? Web? WPF? Something else?
I'm happy with VS2013, not sure if the performance issues some have experienced with VS2015 have been sorted out.
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I'm unsure if I should stay in VS2013 or go forward to VS2015. The project will initially be a lot of back-end components but there's an 83.6% chance of it going web faced.
veni bibi saltavi
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I'd say it depends on whether you will use any of the new features / improvements that VS2015 offers.
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