SOLUTION: Mary rides her bike to john's house, she returns the same way. She rides at a constant speed of 9 mph on level ground, she rides 6 mph going up hill and 18 mph going down hill. her
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Question 671841: Mary rides her bike to john's house, she returns the same way. She rides at a constant speed of 9 mph on level ground, she rides 6 mph going up hill and 18 mph going down hill. her total travel time is 1 hour, how far did she ride?
There is no information about the proportions of the trip, either coming or going, that are level, uphill, or downhill. Does it matter? If the whole trip were level, then in 1 hour she would travel 9 miles at 9 miles per hour. But what about the other extreme. Let's say that the destination is on a continuous upslope from the start. That means she goes uphill all the way going outbound and downhill all the way going outbound. Let represent the one-way distance.
Distance divided by rate is time, so:
The outbound trip is
and the return trip is
A little algebra music, Sammy:
So that is 4.5 miles one direction and 4.5 miles the other direction. That makes the same 9 miles we got when the terrain was flat. 9 miles total travelled regardless of the terrain.
John
My calculator said it, I believe it, that settles it
