Question 409828
{{{s}}} = speed of super-prop
{{{j}}} = speed of turbo-jet
{{{t}}} = time for super-prop to go 2800  mi
given:
(1) {{{j = s + 50}}}
(2) {{{2000 = j*(t - 3)}}}
(3) {{{2800 = s*t}}}
This is 3 equations and 3 unknowns, so it's solvable
Substitute (1) in (2)
(2) {{{2000 = (s + 50)*(t - 3)}}}
(2) {{{2000 = s*t + 50t  - 3s - 150}}}
Substitute (3) in (2)
(2) {{{2000 = 2800 + 50*(2800/s) - 3s - 150}}}
(2) {{{3s = 2800 - 2000 - 150 + 50*(2800/s)}}}
(2) {{{3s = 650 + 50*(2800/s)}}}
(2) {{{3s^2 = 650s + 140000}}}
(2) {{{3s^2 - 650s - 140000= 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 3}}}
{{{b = -650}}}
{{{c = -140000}}
{{{s = (-(-650) +- sqrt( (-650)^2-4*3*(-140000) ))/(2*3) }}}
{{{s = ( 650 +- sqrt(  422500 + 1680000 ))/ 6 }}}
{{{s = ( 650 +- sqrt(  2102500 ))/ 6 }}}
{{{s = ( 650 +- 1450)/ 6 }}}
{{{s = 2100/6}}}
{{{s = 350}}}
and, since
(1) {{{j = s + 50}}}
(1) {{{j = 400}}}
The turbo-jet has a speed of 400 mi/hr
The super-prop has a speed of 350 mi/hr
check answer:
(2) {{{2000 = (s + 50)*(t - 3)}}}
(2) {{{2000 = (350 + 50)*(t - 3)}}}
(2) {{{2000/400 = t - 3}}}
(2) {{{t = 5 + 3}}}
(2) {{{t = 8}}} hrs
and
(3) {{{2800 = s*t}}}
(3) {{{2800 = 350*8}}}
(3) {{{2800 = 2800}}}
OK