Question 1021896
 A car made a journey of 144 miles, stopping for one hour along the way.
 Had it travelled at an average speed 4 mph faster and stopped for one and a half hours, it would have taken the same time.
:
let s = actual speed
then
(s+ 4) = the faster speed
:
Write time equation; time dist/speed
{{{144/s}}} + 1 = {{{144/((s+4))}}} + 1.5
subtract 1 from both sides
{{{144/s}}} = {{{144/((s+4))}}} + .5
multiply the equation by s(s+4)
s(s+4)*{{{144/s}}} = s(s+4)*{{{144/((s+4))}}} + .5s(s+4)
cancel the denominators
144(s+4) = 144s + .5s^2 + 2s
144s + 576 = 144s + .5s^2 + 2s
subtract 144s from both sides
576 = .5s^2 + 2s
Form a quadratic equation on the right
0 = .5s^2 + 2s - 576
Use the quadratic formula;
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
 a=.5; b=2; c=-576
{{{s = (-2 +- sqrt( 2^2-4*.5*-576 ))/(2*.5) }}}
You can do the math, I got a positive solution of
s = 32 mph
:
:
:
See if the checks out in the original equation
{{{144/32}}} + 1 = {{{144/36}}} + 1.5
4.5 + 1 = 4 + 1.5