SOLUTION: Mary rides her bicycle to her friend Amy's house and returns home by the same route. Mary rides her bike at constant speeds of 6mph on level ground, 4mph when going uphill and 12m

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Question 76682: Mary rides her bicycle to her friend Amy's house and returns home by the same route. Mary rides her bike at constant speeds of 6mph on level ground, 4mph when going uphill and 12mph when going downhill. If her total riding time was 2 hours, how far is it to Amy's house?
Answer by ankor@dixie-net.com(12700) About Me  (Show Source):
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Mary rides her bicycle to her friend Amy's house and returns home by the same route. Mary rides her bike at constant speeds of 6 mph on level ground, 4 mph when going uphill and 12 mph when going downhill. If her total riding time was 2 hours, how far is it to Amy's house?
:
Let x = distance one way distance on level ground
Let d = distance from Mary to Amy's house
Then hill dist = (d-x)
:
Write a time equation; Time = distance/speed:
:
level time + uphill time + downhill time + level time = 2hr
x%2F6 + %28%28d-x%29%29%2F4 + %28%28d-x%29%29%2F12 + x%2F6 = 2
Multiply equation by 12
2x + 3(d-x) + (d-x) + 2x = 12(2)
:
4x + 3d - 3x + d - x = 24
:
4x - 3x - x + 3d + d = 24
:
4d = 24
d = 24/4
d = 6 mi from Mary to Amy's house
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