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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie

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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie  [#permalink]

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New post 27 Mar 2016, 19:24
tricky one...definitely D.
i made the mistake to assume that if B won, then the time combined for the girls is 4.5hours..but no one finished faster than in 2.5 hours..so B for sure did not win the race.
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie  [#permalink]

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New post 29 May 2017, 16:06
arps wrote:
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie
II. Regine
III. Brian

A. I only
B. II only
C. III
D. only I or II only
E. I, II, or III

Maximum speed ran= 8 miles/hr. So minimum time for anyone to complete the race=2.5 hrs

Let us assume Brian won the race. So he takes at least 2.5 hrs. Combined time taken by Stephanie and Regine is 2.5+2=4.5 which means one of them timed less than 2.25 or both could have timed 2.25 which contradicts our assumption. So Brian could not have won the race.

There is nothing in the info that separates Regine and Stephanie. So we are left with choice D.
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie  [#permalink]

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New post 08 Jan 2018, 18:07
I feel an algebraic solution makes it crystal clear as to why Brian can never win.

The minimum time it takes Stephanie is 2.5 So let her actual time be 2.5+x where x is 0 or greater.
The time it takes Regine is 2.5 +y where y is 0 or greater. So the time it takes Brian is 3+x+y

Now let's compare 2.5+x to 3+x+y

After some manipulation we obatin
0 compared to Brian's time of y+1/2.

Now y+1/2 will ALWAYS be greater than 0 since y is 0 at a minimum. We can do the same thing with Regine's time. So what this tells us is that Brian will actually always finish behind both Stephanie and Regine by a minimum of 1/2 an hour.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie  [#permalink]

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New post 07 Oct 2018, 07:12
jakolik wrote:
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie
II. Regine
III. Brian

(A) I only
(B) II only
(C) III only
(D) I or II only
(E) I, II, or III


There is a lot to learn here.(analyze )

If the max speed can be 8 miles/her for a race of 20 miles then the MIN time (and not the max time ) will be 20/8 =2.5 hours.Earlier I was assuming as max time.Just imagine now time cannot be less than 2.5 hours else this would mean speed will be more than 8 miles .So solution approach now..suppose speed of brian is max and hence time taken by him would be 2.5 hours.Now this would leave us 4.5 hours as the combined speed (imagine their equation s+r=b+2) now this means suppose one takes 2.5 hours ,then other will take 2 hours which is not possible ..both cannot be 2.25 ..since speed time taken if reduces by 2.5 hours(min time) then speed will increase beyond 8 miles.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie &nbs [#permalink] 07 Oct 2018, 07:12

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