Question 1023678
Convert all minutes to hours:
{{{ 48/60 = 4/5 }}}
{{{ 4/5 = .8 }}}
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{{{ 40/60 = .667 }}}
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Let {{{ d }}} = the distance between the towns
Let {{{ s }}} = the speed of the slower train in mi/hr
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Equation for the faster train:
(1) {{{ d = ( s + 26 )*2.8 }}}
Equation for the slower train:
(2) {{{ d = s*4.667 }}}
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By substitution:
{{{ ( s + 26 )*2.8 = s*4.667 }}}
{{{ 2.8s + 72.8 = 4.667s }}}
{{{ 1.867s = 72.8 }}}
{{{ s = 39 }}} mi/hr
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(1) {{{ d = ( s + 26 )*2.8 }}}
(1) {{{ d = ( 39 + 26 )*2.8 }}}
(1) {{{ d = 182 }}} mi
The distance between the towns is 182 mi
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check:
(2) {{{ d = s*4.667 }}}
(2) {{{ d = 39*4.667 }}}
(2) {{{ d = 182 }}} mi
OK