Question 1150145
Let {{{ s }}} = the speed of the minivan in mi/hr
{{{ s + 5 }}} = the speed of the car in mi/hr
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From 8:30AM to 3:30 PM is 7 hrs
The minivan's head start is {{{ s*(1/2) }}} mi
Let {{{ d[1] }}} = the distance the car travels from
8:30 until it catches the minivan at 3:30 PM
Start a stopwatch when the car leaves at 8:30
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Equation for the minivan:
(1) {{{ d[1] - .5s  = s*7  }}}
Equation for the car:
(2) {{{ d[1] = ( s + 5 )*7 }}}
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Plug (2) into (1)
(1) {{{ ( s + 5 )*7 - .5s = 7s }}}
(1) {{{ 7s + 35 - .5s = 7s }}}
(1) {{{ .5s = 35 }}}
(1) {{{ s = 70 }}}
and
{{{ s + 5 = 75 }}}
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The car's speed is 75 mi/hr
The minivan's speed is 70 mi/hr
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check answer:
(1) {{{ d[1] - .5s  = s*7  }}}
(1) {{{ d[1] - .5*70 = 70*7 }}}
(1) {{{ d[1] = 490 + 35 }}}
(1) {{{ d[1] = 525 }}}
and
(2) {{{ d[1] = ( s + 5 )*7 }}}
(2) {{{ d[1] = 75*7 }}}
(2) {{{ d[1] = 525 }}}
OK