Problema Solution
Legolas ran twice as fast as Frodo in the Rivendell Marathon
after 3 minutes, Legolas was 1500 feet ahead of Frodo.
If Frodo ran at the rate of x feet per minute, at what rate did Legolas run?
Answer provided by our tutors
let frodo's rate be x feet / minute
Legolas ran at twice the speed of Frodo.
Legolas ran at 2x feet / minute.
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Distance run = rate * time
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Frodo's rate = x
time run = 3 minutes
so distance run in first 3 minutes = 3*x feet = 3x feet.
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Legolas's rate = 2x feet/minute
time run = 3 minutes
so distance run = 2x*3= 6x feet
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In the first 3 minutes legolas is 1500 feet ahead.
Distance run by Legolas minus distance run by Fred = 1500
6x-3x=1500
3x=1500
divide by 3
3x/3 = 1500/3
x=500 feet/ minute.
In 3 minutes Frodo ran 500*3 = 1500 feet.
Legolas ran 6x feet = 6*500= 3000 feet
Frodo 1500 feet
Legolas 3000 feet.
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