

Too easy, even by [UK] year 6 standards!
10+15 = 25 mph.
bikes meet = 100/25 = 4 hours
Mosquito travels = 4 * 20 = 80 miles.
veni bibi saltavi





Damn, sixth graders can do infinite sums? It's pretty obvious what that sum converges to (based on the length of time the mosquito has to fly in total), but I can see that frying some brains in the process.






time(t)=distance(x)/Velocity(v)
v1=15mph > Velocity of faster bike
v2=10mph > Velocity of slower bike
t1=x/15 t2=x100/10
t1=t2 > when they meet
x/15 = x100/10
x=40 miles
t1=t2=4h
Mosquito travelled = 4 * 20 = 80 miles





Member 12063711 wrote: time(t)=distance(x)/Velocity(v)
v1=15mph > Velocity of faster bike
v2=10mph > Velocity of slower bike
t1=x/15 t2=x100/10
t1=t2 > when they meet
x/15 = x100/10
x=40 miles
t1=t2=4h
You do know that your equation's wrong and that your answer based on even some of that is wrong?
x=60 not 40, to start
and it should be t2=(100x)/10 or it would evaluate to a negative value and/or you're missing parenthesis so it really evaluates to x/15=x10 and that's not going to work out well, either.
Ravings en masse^ 
"The difference between genius and stupidity is that genius has its limits."  Albert Einstein 
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure."  Balboos HaGadol Mar 2010 





Before looking at any of the answers, below, I simply looked at all of the information. The two bikes will travel for four hours until they meet
 so at 20mph the misquito will travel 80 miles if you're interested in flight.
 The misquito will only travel 40 miles if you only consider it's starting point and final destination.
I did have an edge. I done graduated from sixth grade!
Ravings en masse^ 
"The difference between genius and stupidity is that genius has its limits."  Albert Einstein 
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure."  Balboos HaGadol Mar 2010 





Great way to get your homework done for you.





How can a mosquito change velocity from +20mph to 20mph without slowing down?
=========================================================
I'm an optoholic  my glass is always half full of vodka.
=========================================================





Teleportation. It only changes direction.





Low inertia and a tiny trampoline fixed to each bike.
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...





What's the last thing that goes through the flies mind when it hits the trampoline?





55378008 wrote: What's the last thing that goes through the flies mind when it hits the trampoline?
A very old joke?
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...






OriginalGriff wrote: Low Zero inertia
FTFY
... such stuff as dreams are made on





hmmm, fly mosquito swat ?





It's easy: Inertial dampeners





What's the last thing to go through a mosquito's mind when it hits a bicycle travelling at a combined speed of 35mph? It's a***hole!
=========================================================
I'm an optoholic  my glass is always half full of vodka.
=========================================================





About 13 miles[^].
And I won't comment the speed.





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!





What you didn't mention is that the mosquito is actually an omnipresent alien space mosquito spanning galaxies in size.
Only the mighty mosquito knows the answer...





Bassam AbdulBaki 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.





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 16hrs ago.





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...)





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 ?





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



