Question 103605
To get to work Sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. If the train goes 40 km per hour faster than Sam's constant rate of jogging and the entire trip takes 1/2 hour how fast does Sam jog?
:
Let s = his jogging speed
then
(s+40) = train speed
:
Write a time equation: Time = Distance/speed
:
jog time + train time = .5 hrs
{{{3/s}}} + {{{5/((s+40))}}} = .5
:
Multiply equation by s(s+40) and you have:
3(s+40) + 5s = .5(s(s+40))
:
3s + 120 + 5s = .5s^2 + 20s
:
8s + 120 = .5s^2 + 20s
:
0 = .5s^2 + 20s - 8s - 120
:
.5s^2 + 12s - 120 = 0; a quadratic equation
:
Use the quadratic formula to find s: a=.5; b=12; c=-120
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{s = (-12 +- sqrt( 12^2 - 4 * .5 * -120))/(2*.5) }}}
:
{{{s = (-12 +- sqrt(144 - (-240) ))/(1) }}}
:
{{{s = (-12 +- sqrt(144 + 240 )) }}}
:
{{{s = -12 +- sqrt(384 ) }}}
:
s = -12 + 19.5959; we only need the positive solution here
:
s = +7.5959 km/hr is his jogging speed
:
:
Check solution by finding the time
{{{3/7.6}}} + {{{5/47.6}}} =
   .394 + .105  = .499 ~ .5 hrs
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Did this make sense to you? Any questions?