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 304523: 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 ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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?
:
Let t = total time for the round trip
then using the distance equation dist = speed * time
2(.6t )= 1.2t distance one way
:
Find the speed (s) down hill, using a distance equation
s(.4t) = 1.2t
.4st = 1.2t
Divide by t
.4s = 1.2
s = 1.2%2F.4
s = 3 mph down hill speed
:
Find the average speed (a) using a time equation
%28.6t%29%2F2 + %28.4t%29%2F3 = t%2Fa
multiply by 6a
3a(.6t) + 2a(.4t) = 6t
:
1.8at + .8at = 6t
2.6at = 6t
Divide both sides by t
2.6a = 6
a = 6%2F2.6
a = 2.31 mph is the average speed
:
:
Check solution
%28.6t%29%2F2 + %28.4t%29%2F3 = t%2F2.3
Divide thru by t
%28.6%29%2F2 + %28.4%29%2F3 = 1%2F2.31
.3 + .133 = .433
:
I can't seem to come up with one the given solutions???