SOLUTION: Vera walked from her home to a friend's home at a rate of 3 miles per hour. She rode to work with her friend at an average rate of 30 miles per hour. It took Vera a total of 50 min

Question 520471: Vera walked from her home to a friend's home at a rate of 3 miles per hour. She rode to work with her friend at an average rate of 30 miles per hour. It took Vera a total of 50 minutes (5/6 of an hour) to walk to her friend's home and to get to work, traveling a total distance of 16 miles. How long did she walk and how long did she ride with her friend to get to work?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Vera walked from her home to a friend's home at a rate of 3 miles per hour.
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She rode to work with her friend at an average rate of 30 miles per hour.
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It took Vera a total of 50 minutes (5/6 of an hour) to walk to her friend's home and to get to work, traveling a total distance of 16 miles.
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How long did she walk and how long did she ride with her friend to get to work?
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Walking DATA:
rate = 3 mph ; time = x hrs ; distance = rt = 3x miles
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Riding DATA:
rate = 30 mph ; time = (5/6)-x hrs ; distance = rt = 30[(5/6)-x]
= (5*5)-30x miles
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Equation:
distance + distance = 16 miles
3x + 25 - 30x = 16
-27x = -9
x = 1/3 hrs (walking time)
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(5/6) - (1/3) = (5/6)-(2/6) = 1/2 hrs (riding time)
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Cheers,
Stan H.
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