Question 815208
Think of this as Jane standing still and
Peter moving away from her at the sum of their speeds
Let Jane's speed in mi/hr = {{{ s }}}
Peter's speed = {{{ s + 15 }}}
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When Peter is 225 mi from Jane:
{{{ 225 = ( s + s + 15 )*3 }}}
{{{ 225 = ( 2s + 15 )*3 }}}
{{{ 6s + 45 = 225 }}}
{{{ 6s = 180 }}}
{{{ s = 30 }}}
{{{ s + 15 = 45 }}}
Jane's rate is 30 mi/hr
Peter's rate is 45 mi/hr
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Average speed = ( total distance ) / ( total time )
Let {{{ d }}} = distance from home to city
{{{ 15 = d / t[1] }}}
{{{ d = 15t[1] }}} mi
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Going back home:
{{{ 15t[1] = 35*t[2] }}}
{{{ 3*t[1] = 7t[2]
{{{ t[2] = (3/7)*t[1] }}}
also:
{{{ t[1] + t[2]= 2 }}}
By substitution:
{{{ t[1] + (3/7)*t[1] = 2 }}}
{{{ t[1]( 7/7 + 3/7 ) = 2 }}}
{{{ t[1]*( 7 + 3 ) = 14 }}}
{{{ t[1] = 14/10 }}}
{{{ t[1] = 7/5 }}}
{{{ t[1] = 1.4 }}}
{{{ .4*60 = 24 }}}
Her time going to the store was 1 hr 24 min