SOLUTION: Question- Legolas ran twice as fast as Frodo in the Rivendell Marathon. After 3 minutes, Legolas was 1500 feet ahead of Frodo. a) If Frodo ran at the rate of x feet

Question 325578: Question- Legolas ran twice as fast as Frodo in the Rivendell Marathon.
After 3 minutes, Legolas was 1500 feet ahead of Frodo.
a) If Frodo ran at the rate of x feet per minute, at what rate did Legolas run?
b) Draw a diagram to represent the problem.
c) Use the information in your diagram to write the equation.
d) Solve the equation for x
e) How far did each one run during the first 3 minutes?
Legolas:__________
Frodo:_________
This was a test question sent to me by my daughter's teacher, she didn't do so well. I do not have the math skills to help her with this and would appreciate your assistance so I may be able to assist her. Thank you for your time and patience. This was submitted before but was unable to locate in solved or unsolved problems. BGR
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let frodo's rate be x feet / minute
Legolas ran at twice the speed of Frodo.
Legolas ran at 2x feet / minute.
..
Distance run = rate * time
..
Frodo's rate = x
time run = 3 minutes
so distance run in first 3 minutes = 3*x feet = 3x feet.
..
Legolas's rate = 2x feet/minute
time run = 3 minutes
so distance run = 2x*3= 6x feet
..
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.
..
A|__________________________|B_______________________|C

AB = 3x run by frodo
AC = 6x = run by Legolas
BC= 1500
..
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