Question 957091
Biking from home, ave. speed = {{{ r }}}
Biking back home, ave. speed = {{{ r + 3 }}}
(a)
{{{ 50 = r*t[1] }}}
{{{ t[1] = 50/r }}}
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{{{ 50 = ( r + 3 )*t[2] }}}
{{{ t[2] = 50/( r+3 ) }}}
{{{ t[1] + t[2] = 50/r + 50/( r+3 ) }}}
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(b)
{{{ t[1] = 50/15 }}}
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{{{ t[2] = 50/( 15 + 3 )
{{{ t[2] = 50/18 }}}
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{{{ t[1] + t[2] = 50/15 + 50/18 }}}
{{{ t[1] + t[2] = (50/3)*( 1/5 + 1/6 ) }}}
{{{ t[1] + t[2] = ( 50/3)*( 6/30 + 5/30 ) }}}
{{{ t[1] + t[2] = ( 50/3 )*( 11/30) }}}
{{{ t[1] + t[2] = ( 5/3 )*( 11/3 ) }}}
{{{ t[1] + t[2] = 55/9 }}}
{{{ t[1] + t[2] = 6.1 }}} hrs
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(c)
{{{ t[1] + t[2] = 50/12 + 50/15 }}}
{{{ t[1] + t[2] = 25/6 + 20/6 }}}
{{{ t[1] + t[2] = 45/6 }}}
{{{ t[1] + t[2] = 15/2 }}}
{{{ t[1] + t[2] = 7.5 }}}
{{{ 7.5 - 6.1 = 1.4 }}} hrs longer
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Hope I got these