Question 1050546
Let {{{ t }}} = time in hrs to drive 144 mi
on the 2nd day
{{{ t + 2 }}} = time to drive 240 mi on the
1st day
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His rate on the 1st day:
(1) {{{ r = 240/( t + 2 ) }}}
His rate on the 2nd day:
(2) {{{ r = 144/t }}}
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Substitute (2) into (1)
(1) {{{ 144/t = 240/( t + 2 ) }}}
Multiply both sides by {{{ t*( t+2 ) }}}
(1) {{{ 144*( t+2 ) = 240t }}}
(1) {{{ 144t + 288 = 240t }}}
(1) {{{ 96t = 288 }}}
(1) {{{ t = 3 }}}
and
{{{ t + 2  = 5 }}}
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On the 1st day, he drove for 5 hrs
On the 2nd day, he drove for 3 hrs
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check:
(2) {{{ r = 144/t }}}
(2) {{{ r = 144/3 }}}
(2) {{{ r = 48 }}} mi/hr
and
(1) {{{ r = 240/( t+2 ) }}}
(1) {{{ r = 240/5 }}}
(1) {{{ r = 48 }}} mi/hr
OK