# math

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betty,cathy,isabel,lani,alma,and ursula ran an 800meter race. alma beat isabel by 7 meters. ursula beat betty by 12 meters. alma finished 5 meters ahead of lani but 3 meters behind ursula. cathy finished halfway between the 1st and last girl. In what order did they finish? what were the distances between each girl?

• math -

It will not be complicated if we write down the information mathematically.
Let the initial of each person represent the distance in metres ahead of the last athelete.
Then according to the question:
A-I = 7
U-B = 12
A-L = 5
U-A = 3
Disregard Cathy for the moment.

We can tell that Ursula is ahead of everyone, and Alma is second, since there is only ursula ahead of her. Since A-L=5 and A-I=7, we conclude that Lani is ahead of Isabel.
The order is thus, after applying the distances
U=12
A=9
L=4
I=2
B=0
Now we can insert Cathy being (U+B)/2=6, between Alma and Lani.

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