SOLUTION: Davin and Iris decided to run at a heart-shaped track with a perimeter of 1600 meters. They start at the same point and run in opposite directions. If the ratio of Davin's speed to

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Davin and Iris decided to run at a heart-shaped track with a perimeter of 1600 meters. They start at the same point and run in opposite directions. If the ratio of Davin's speed to      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 485927: Davin and Iris decided to run at a heart-shaped track with a perimeter of 1600 meters. They start at the same point and run in opposite directions. If the ratio of Davin's speed to Iris's speed is 3:2 and they meet again after 8 minutes, how fast is Davin in meters per minute?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Davin and Iris decided to run at a heart-shaped track with a perimeter of 1600 meters.
They start at the same point and run in opposite directions.
If the ratio of Davin's speed to Iris's speed is 3:2 and they meet again after 8 minutes, how fast is Davin in meters per minute?
:
let D = Devin's speed in met/min
let I = Iris's speed
:
When they meet they will have run a total of 1600 meters
Write a distance equation, dist = time * speed
:
D's dist + I's dist = 1600
8D + 8I = 1600
simplify, divide by 8
D + I = 200
I = (200-D); we can use this form for substitution
:
It says,"the ratio of Davin's speed to Iris's speed is 3:2 "
D%2FI = 3%2F2
substitute (200-D) for I
D%2F%28200-D%29 = 3%2F2
Cross multiply
2D = 3(200-D)
2D = 600 - 3D
2D + 3D = 600
D = 600%2F5
D = 120 met/min is Devin's speed
:
:
Check solution by finding the dist each runs (I's speed: 200-120 = 80 met/min)
8(120) = 960
8(80) = 640
--------------
totals: 1600 m, confirms our solution