Question 761845
The father had a head start of 30 min
In terms of distance his head start was
{{{ d[1] = 24*(1/2) }}}
{{{ d[1] = 12 }}} mi
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Start a stopwatch when the Son leaves
Let {{{ t }}} = time on stopwatch when
Son catches Father
Let {{{ d }}} = distance that Son travels
until he catches Father
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Father's equation:
{{{ d - 12 = 24t }}}
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Son's equation:
{{{ d = 40t }}}
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By substitution:
{{{ 40t - 12  = 24t }}}
{{{ 16t = 12 }}}
{{{ t = .75 }}} hrs
{{{ .75*60 = 45 }}} min
It took the Son 45 min to catch the bus
check:
{{{ d = 40t }}}
{{{ d = 40*.75 }}}
{{{ d = 30 }}}
and
{{{ d - 12 = 24t }}}
{{{ d - 12 = 24*.75 }}}
{{{ d = 12 + 18 }}}
{{{ d = 30 }}}
OK