<PRE><B>Question 422594</B>
A jogger ran 6 miles up a hill and 10 miles on level ground.
He ran 2mph faster on level ground than on the hill.
 If the total trip lasted 4 hours, how fast did he run uphill?
:
Let s = speed run uphill
then
(s+2) = speed on level ground
:
write a time equation, time = dist/speed
:
uphill time + level ground time = 4 hrs
{{{6/s}}} + {{{10/((s+2))}}} = 4
multiply by s(s+2)
s(s+2)*{{{6/s}}} + s(s+2)*{{{10/((s+2))}}} = 4s(s+2)
:
cancel the denominators
6(s+2) + 10x = 4s(s+2)
:
6s + 12 + 10s = 4s^2 + 8s
:
Combine on the right
0 = 4s^2 + 8s - 6s - 10s - 12
:
a quadratic equation
4s^2 - 8s - 12 = 0
:
Simplify, divide by 4
s^2 - 2s - 3 = 0
factor to
(s - 3)(s + 1) = 0
the positive solution
s = 3 mph up hill
:
:
Check this by finding the actual time of each (5 mph is speed on level ground)
6/3 + 10/5 = 4
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