“Lewis and Carol travel together on a road from A to B, then return on the same road, with the entire trip taking 3 hours. Sometimes that road goes uphill, sometimes downhill, and sometimes it is level. When the road goes uphill, their rate is 40 mph; downhill their rate is 60 mph; on level road, their rate is x mph.”
Even if you were given a numerical value for x, the distance from A to B would (in most cases) not be uniquely determined. But there is one value for x that would determine that distance uniquely. Compute this value of x [Note: uphill going is downhill returning!]
Credits – Southern California ARML, Oct. 2009, Team round
Original post here.
Solution follows.
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Let 
This equation can be simplified to:
Or, multiplying both sides by 24:
The only value of 
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