Hi Sri,
This IR question is essentially about the Distance Formula (Distance = Rate x Time) and making sure that you take enough notes.
We're told that the race is 100 miles and that it's broken in HALVES (50 miles each). The question gives us the rates for both Jess and Kerri during the FIRST HALF of the race (5mph and 6mph, respectively) and during the SECOND HALF of the race (8mph and 6mph, respectively).
The first question asks HOW FAR ahead is Kerri when she reaches the half-way point. Since that is the "50 mile" measure, we can figure out how long it took Kerri to get to that point:
D = R x T
50mi = 6mph x T
50/6 = T
8 1/3 hrs = T
Now that we have the time, we can figure out how far Jess traveled in 8 1/3 hours…
D = (5mph) x (8 1/3 hours)
D = 41 2/3 miles
This means that when Kerri is at the 50 mile mark, Jess is at 41 2/3 miles. The difference is approximately 8 MILES
The second question asks how many miles Jess finishes ahead of Kerri. This means that at some point Jess PASSES Kerri and finishes the race first. So, let's calculate how long it took Jess to finish the race.
First part (50 miles at 5mph):
D = R x T
50mi = (5mph) x (T)
50/5 = T
10hrs = T
Second part (50 miles at 8mph):
D = R x T
50mi = (8mph) x (T)
50/8 = T
6 1/4hrs = T
Jess's total time = 10 + 6 1/4 = 16 1/4 hours to finish the race.
Since Kerri's speed was constant (6mph), we can figure out how far she went in 16 1/4 hours:
D = R x T
D = (6mph) x (16 1/4hrs)
D = 97 1/2 miles
So, Jess is approximately 3 MILES ahead of Kerri when Jess finishes the race.
GMAT assassins aren't born, they're made,
Rich
