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 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?
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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/6}}} + {{{((d-x))/4}}} + {{{((d-x))/12}}} + {{{x/6}}} = 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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