Question 596396
L:et {{{ t }}} = the same time for both trains in hours
Let {{{ s }}} = the speed of the express train in mi/hr
{{{ s - 20 }}} = the speed of the freight train in mi/hr
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Equation for express train:
(1) {{{ 150 = s*t }}}
Equation for freight train:
(2) {{{ 100 = ( s - 20 )*t }}}
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(2) {{{ 100 = s*t - 20t }}}
Substitute (1) into (2)
(2) {{{ 100 = 150 - 20t }}}
(2) {{{ 20t = 150 - 100 }}}
(2) {{{ 20t = 50 }}}
(2) {{{ t = 2.5 }}} hrs
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(1) {{{ 150 = s*t }}}
(1) {{{ 150 = s*2.5 }}}
(1) {{{ s = 150/2.5 }}}
(1) {{{ s = 60 }}} mi/hr
and
(2) {{{ 100 = ( s - 20 )*t }}}
(2) {{{ 100 = ( s - 20 )*2.5 }}}
(2) {{{ 100 / 2.5 = s - 20 }}}
(2) {{{ s - 20 = 40 }}}
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The average speed of the express train in 60 mi/hr
The average speed of the freight train in 40 mi/hr