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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
2
Kudos
Timing for each distance:
D1=500,000 miles, v1= 100mph and t1=D1/v1= 5 hours
D2=250,000 miles, v2= 200mph and t2=D2/v2= 1.25 hours
D3=125,000 miles, v3= 400mph and t3=D3/v3= 0.3125 hours, et cetera.

D (Total Distance) = 1,000,000 miles.
T (Total Time) = 5 + 1.25 + 0.3125 +... = 5/(1-0.25) = 20/3 hours.
Thus, v (average speed) = D / T = 150,000 mph

Final answer is (D)
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
2
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Average Speed = Distance / Time
we need to determine the total distance.
Time to reach earth = 500,000/100,000 + 250,000/200,000 + 125,000/400,000 + 62,500/800,000 + 31,250/1,600,000 +...
=5 + 5/4 + 5/16 + 5/64 + ...
=5(1+1/4+1/16+1/64+...)
So we can look at this as an infinite geometric series.
common ratio = 1/4
so S=S1/(1-r) = 5/(1-1/4) = 5/(3/4) = 20/3
Hence Time taken = 20/3

Average Speed = 1,000,000/(20/3)= 3*50,000 = 150,000mph

The answer is option D.
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
1
Kudos
let d=1,000,000 miles, s=100,000 miles per hour
average speed= total distance/total time
= d/(d/2s)+(d/8s)+......= d/[d/s(1/2+1/8+1/32........)]
here denominator is a infinite GP series...whose sum = a/1-r
= (1/2)/(1-1/4) = 2/3
average speed= 3s/2=150,000 miles per hour

OA:D
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
Given:
1. Aliens who live 1,000,000 miles from Earth decide to come to our planet for a visit. They program their space shuttle to travel 100,000 miles per hour for the first 500,000 miles, 200,000 miles per hour for the next 250,000 miles, 400,000 miles for the next 125,000 miles and so on, doubling the speed every time half of the remaining distance is covered.

Asked: If this pattern is maintained until the aliens reach earth, what will their average speed for the trip be in miles per hour?

Total distance travelled = 1,000,000 miles

Total time taken = 5 + 5/4 + 5/4^2 + .... = 5/(1-1/4) = 5*4/3 = 20/3 hrs

Average speed = 1000,000 miles / (20/3) hrs = 3000,000/20 = 150,000 miles/hrs

IMO D
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
Hi all,

I adopted this method:

Distance = D
Initial Speed = S = 100.000 m/h
Avg Speed = M

D/M = (D/2)/(S) + (D/4)/(S/2) + (D/8)/(S/4) + ... = D/S * (1/2 + 1/2 + 1/2 + ...) = D/S * 1/2 * n

M= S * 1/2 * n = 50.000 * n

Regardless n, the only multiple of 50 goes with answer D

Thanks
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
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Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane [#permalink]
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