Toughie

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by Prashant Ranjan » Mon Sep 10, 2012 12:27 pm
We don't who has won the race and who has come last. All we know is the fastest time is 2.5 hrs and the fastest speed is 8mi/hr.
Let's us assume that Brain won the race. He took 2.5 hrs to complete the race. In this case
S + R = 4.5
Now the minimum possible time S and R could have taken would be 2.25 hrs to complete the race, since if they took any time less than 2.25 hrs (which is already less than 2.5hrs), then it would mean that Brian wasn't the first to win the race.

Note that if S (or R) took more than 2.5 hrs, it means R (or S) took less than 2.5 hrs, and hence Brian wouldn't be winner in that case.
Now even if they took 2.25 hrs, still the case is not possible, because Brian needs to take the lowest time in order to be winner. So we come to conclusion that Brian cannot be a winner in any case.

Let's assume that Stephanie won the race in record time of 2.5 hrs. In that case
B = R + 0.5
Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.
The same is true with
B = S + 0.5
R came first, S and then B.
So we see that B is a loser in any case, however R or S have equal chances to win.
So (D) is the answer.

Thanks
Prashant