SOLUTION: While hiking the Peralta Trail to Wheeler’s Needle and back, Rick spent 60% of his time walking uphill to Wheeler’s Needle and 40% of his time returning by the same trail. If he a

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Question 304549: While hiking the Peralta Trail to Wheeler’s Needle and back, Rick spent 60% of his time walking uphill to Wheeler’s Needle and 40% of his time returning by the same trail. If he averaged 2 miles per hour uphill, what was his average speed for the round-trip?
A. 2 1/3 mph B. 2.25 mph C. 2.4 mph D. 2.5 mph E. 2.6 mph

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = his time walking uphill
The ratio (time walking uphill)/(time walking downhill) = 60%2F40
t/(time walking downhill) = 3%2F2
%282%2F3%29%2At = time walking downhill
For uphill:
d+=+2t
For downhill:
d+=+r%5Bd%5D%2A%282%2F3%29%2At
r%5Bd%5D%2A%282%2F3%29%2At+=+2t
r%5Bd%5D+=+1%2F%281%2F3%29
r%5Bd%5D+=+3 mi/hr
------------------
The average speed is (total distance)/(total time)
Total distance = d+%2B+d+=+2d
The time for uphill = t+=+d%2F2
The time for downhill = %282%2F3%29%2At+=+d%2F3
2d+%2F+%28d%2F2+%2B+d%2F3%29+=+2%2F%283%2F6+%2B+2%2F6%29
2%2F%285%2F6%29+=+12%2F5
2.4 mi/hr