Two trains,each having a speed of 30km/h, are headed at each other on the same straight track.A bird that can fly at 60km/h flies off the front of one of the train when they are 60 Km apart and heads directly back to the first train,the bird flies directly back to the first train, and so on.What is the total number of trips the bird can make from one train to the other before they meet?
i didn't get it.. heads directly back to the first train? :O
hey ananthu the ans is infinite only............ See if u consider the trips made by bird one by one, u'll find that the time interval or the distance covered forms an infinte gp with common ratio=1/2
lol infinite gp with common ration 1/2 converges to give a number :P..
ya it gives a number but the question is to count the no of trips made...........Thats y d answer is INFINITE
think logically man.. in one hour the two trains will meet... do you think it ll do INFINITE trips :P.. it ll eventually stop
C'mon dont think too deep. I know it cant happen bt its not a practical life situation......... u understand??????????
it is.. and you ll get a finite number as the answer :)
@dls @yrelhan4 @Vincent-Lyon.Fr try these.. i don't seem to get a proper lead to solve this one :-/
according to what I did.. if n is the number of times it flies.. then the equation that gives the value of n is this \[\frac{8}{9}+ [\frac{8}{9^2} + \frac{8^2}{9^3}+....+\frac{8^n}{9^{n+1}}] = 1\] solve for n.. :D
no thats wrong.. damn.. never mind
I got it.
\[\LARGE \frac{a(1-r^n)}{1-r}\]
no my equation is wrong
its correct
no its wrong :P..
what i figured is.. the bird always takes 8/9th of the remaining time to complete its journey
The time taken is finite, as is the distance travelled by the bird. It is simply 1 hour before the trains meet and distance travelled by the bird is 60x1 = 60 km. But there is an infinite number of trips.
hmpf :-/.. the distance travelled is 60 X 1 = 60 how did you get that? :O
For first trip Vab=90km/hr T1=60/90=2/3 For 2nd trip s=60-(60*2)/3=20km T2=20/90=2/(3)^2 .. Let n t rips be covered.. t1+t2+t3........tn=1 \[\LARGE \frac{2}{3}+\frac{2}{3^2}+\frac{2}{3^3}........\frac{2}{3^n}\] \[\LARGE \frac{a(1-r^n)}{r-1}=\frac{2}{3} \frac{(1-3^n)}{3-1}\]
i messed up 1-r and r-1 ^_^
@Mashy Simply, the bird flies at 60 km/h for one hour (time taken by trains to meet).
oh ok ok .. i get it vincent
i did it wrong?:/
oh Vab is 30 nevermind
can any one please explain how the number of trips made is infinite?
The answer is infinite number of trips. Cant really explain it logocally, but solving dls's equation gives me n=infinity
@yrelhan4 how did my equation give infinity? :O i know the answer is infinite though :|
You have take r=3. its 1/3. So 2/3 [1 + 1/3 + 1/3^2 + ........ + 1/3^n-1 =1 ==> 1-(1/3)^n=1 Solve to get n=infinity
r is 3 only :/ dafuq
oh sorry
nevermind
:O 2/3 2/(3)^2 . you are multiplying the first term by 1/3
\[\LARGE \frac{a(1-r^n)}{1-\frac{1}{3}}=\frac{2}{3} \frac{(1-\frac{1}{3}^n)}{\frac{1}{3}-1}\]
right?
dam 1-1/3*
okay ..so \[\LARGE 1-\frac{1}{3^n}=1\] \[\LARGE \frac{1}{3^n}=0\]
yes. so n-->infinity.
@ananthu96 *
lol. 1/3^infinity=0 3^infinity=infinity.
yeah so 1/3^infinity=0 :P
tu ja na :/ bc
:p
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