Question 304523
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? 
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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/.4}}}
s = 3 mph down hill speed
:
Find the average speed (a) using a time equation
{{{(.6t)/2}}} + {{{(.4t)/3}}} = {{{t/a}}}
multiply by 6a
3a(.6t) + 2a(.4t) = 6t
:
1.8at + .8at = 6t
2.6at = 6t
Divide both sides by t
2.6a = 6
a = {{{6/2.6}}}
a = 2.31 mph is the average speed
:
:
Check solution
{{{(.6t)/2}}} + {{{(.4t)/3}}} = {{{t/2.3}}}
Divide thru by t
{{{(.6)/2}}} + {{{(.4)/3}}} = {{{1/2.31}}}
.3 + .133 = .433

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I can't seem to come up with one the given solutions???