SOLUTION: I need help solving the following equation or how to solve it. Samantha ran on a fitness track for 20 mins. She walked for 10 mins. Her running rate was 250ft per minute faster tha

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Question 781076: I need help solving the following equation or how to solve it. Samantha ran on a fitness track for 20 mins. She walked for 10 mins. Her running rate was 250ft per minute faster than her walking rate. If she ran and walked a total of 15,500ft, how fast did she run?
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Samantha ran on a fitness track for 20 mins. She walked for 10 mins. Her running rate was 250ft per minute faster than her walking rate. If she ran and walked a total of 15,500ft, how fast did she run?
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Equations:
Distance Equation::: r + w = 15,500 ft
Rate Equation::::::: r/(1/5) = w/(1/6) + 250
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Modify for elimination:
6r + 6w = 6*15,500
6r - 5w = 30*250
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Subtract and solve for "w":
11w = 85,500
walking distance = 7772.73 ft
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running dstance = 7727.27 ft
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Cheers,
Stan H.
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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
r=w+250,
20r+10*w=15500
20(w+250)r+10*w=15500
20w+5000+10w=15500
30w=10500
3w=1050
w=350 f/m
r=600 f/m