Question 162021
Joel drives his car for 20km at a certain speed; he increases his speed by 5 km
 per hour and drives for an additional 20km. If the total trip taken.
 is 1 hour, what is his original speed?
:
Let s = his original speed
then
(s+5) = his increased speed
:
Write a time equation; Time = {{{dist/speed}}}
;
Orig speed time + increase speed time = 1 hour
{{{20/s}}} + {{{20/((s+5))}}} = 1
;
Multiply equation by s(s+5), results;
20(s+5) + 20s = s(s+5)
:
20s + 100 + 20x = s^2 + 5s
40s + 100 = s^2 + 5s
:
0 = s^2 + 5s - 40s - 100
A quadratic equation:
s^2 - 35s - 100 = 0
Solve this with the quadratic formula;
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this problem: a=1, b=-35, c=-100
{{{s = (-(-35) +- sqrt(-35^2 - 4*1*-100 ))/(2*1) }}}
{{{s = (35 +- sqrt(1225 + 400 ))/(2) }}}
Do the math here, the positive solution should be:
s = 37.656 km/hr is the original speed
;
:
Check solution on a calc:
20/37.656 + 20/42.656 = .99998 ~ 1