SOLUTION: Mary visits her friend Annie and then returns home by the same route. She walks 2km/h uphill, 6km/h downhill and 3km/h on flat ground. If her total walking time to Annie's house an

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Question 932996: Mary visits her friend Annie and then returns home by the same route. She walks 2km/h uphill, 6km/h downhill and 3km/h on flat ground. If her total walking time to Annie's house and back was 6 hours, then how far from Mary's house does Annie live?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The road from Mary's house to Annie's house has
a total of x km of flat stretches, and
a total of y km of sloping stretches,
for a total distance of x%2By km.
Walking to Annie's house and back, Mary walks a total of
2x km on flat ground,
y km uphill, and
y km downhill.
It takes her 2x%2F3 hours to cover the flat ground stretches,
y%2F2 hours to cover the uphill stretches, and
y%2F6 hours to cover the downhill stretches.
Our equation is
2x%2F3%2By%2F2%2By%2F6=6
Multiplying both sides of the equal sign times 6 we get
6%282x%2F3%2By%2F2%2By%2F6%29=686
6%282x%2F3%29%2B6%28y%2F2%29%2B6%28y%2F6%29=36
4x%2B3y%2By=36
4x%2B4y%29=36
4%28x%2By%29=36
x%2By=36%2F4
highlight%28x%2By=9%29
Annie lives highlight%289%29 km from Mary's house.