SOLUTION: Brittany can run a mile in 6 minutes and Christina can run a mile in 9 minutes. If both Brittany and Christina start running at the same time and Brittany starts 1/3 of a mile behi

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Question 279094: Brittany can run a mile in 6 minutes and Christina can run a mile in 9 minutes. If both Brittany and Christina start running at the same time and Brittany starts 1/3 of a mile behind Christina, how long will it take Brittany to catch up with Christina? I know that Brittany runs at 1/6 miles per minute, Christina runs at 1/9 miles per minute, and distance is rate multiplied by time.
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Brittany can run a mile in 6 minutes and Christina can run a mile in 9 minutes. If both Brittany and Christina start running at the same time and Brittany starts 1/3 of a mile behind Christina, how long will it take Brittany to catch up with Christina?
I know that Brittany runs at 1/6 miles per minute, Christina runs at 1/9 miles per minute, and distance is rate multiplied by time.
-------------------------------------
Brittany DATA:
distance = [x+(1/3)] miles ; rate = (1/6)mi/min ; time = [(3x+1)/3]/(1/6) =
2(3x+1) = 6x+2 min
--------------------------------
Christina DATA;
distance = x mile rate = 1/9 mi/m ; time = x/(1/9) = 9x min
-------------------------------------
Equation:
time = time
6x+2 = 9x
3x = 2
x = 2/3
Brittaney's time = 6 min = Christina's time
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Cheers,
Stan H.

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
brittany 60/6=10 mph
christina 60/9=20/3=6 2/3 mph
60x/6=60x/9+1/3
rt=rt+d
10x=20x/3+1/3
30x=20x+1
10x=1
x=1/10=6 minutes
check
10*1/10=20/3*1/10+1/3
1=2/3+1/3
1=1
ok