Question 617203
Let {{{t}}} = the time for the 1st trip
{{{ 3 - t }}} = time for the 2nd trip
Let {{{ s }}} = the speed for the 1st trip
{{{ s - 5 }}} = the speed for the 2nd trip
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Ist rip:
(1) {{{ 37 = s*t }}}
2nd trip:
(2) {{{ 22 = ( s - 5 )*( 3 - t ) }}}
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(2) {{{ 22 = 3s - 15 - s*t + 5t }}}
From (1):
{{{ t = 37/s }}}
(2) {{{ 22 = 3s - 15 - s*(37/s) + 5*(37/s) }}}
Multiply both sides by {{{ s }}}
(2) {{{ 22s = 3s^2 - 15s - 37s + 185 }}}
(2) {{{ 3s^2 - 52s - 22s + 185 = 0 }}}
(2) {{{ 3s^2 -74s + 185 = 0 }}}
Use quadratic formula to solve for {{{ s }}}