Question 888128
I think the fastest way for all three to get from
A to B is for 2 of them to go by motorbike
while the other 1 is walking, then one of the
two at B turns right around, picks up the walking
backpacker, and takes him to B.
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Let {{{ t[1] }}} = time in hrs for two to get from A to B
on the motorbike
{{{ 60 = 50*t[1] }}}
{{{ t[1] = 6/5 }}} hr
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During this time, the third backpacker has walked
{{{  d[1] = 5*( 6/5 ) }}}
{{{ d[1] = 6 }}} km
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One of them from B turns around and heads toward
the walker
Let {{{ t[2] }}} = time in hrs for them to meet
Let {{{ d[2] }}} = the distance the motorbike travels
until them meet
{{{ ( 60 - 6 ) - d[2] = 54 - d[2] }}} is the distance
the walker travels in that time
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Equation for motorbike:
(1) {{{ d[2] = 50t[2] }}}
Equation for walker:
(2) {{{ 54 - d[2] = 5t[2] }}}
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Substitute (1) into (2)
(2) {{{ 54 - 50t[2] = 5t[2] }}}
(2) {{{ 55t[2] = 54 }}}
(2) {{{ t[2] = 54/55 }}} hrs
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In {{{ 54/55 }}} hrs, the walker has traveled
{{{ d[3] = 5*( 54/55 ) }}}
{{{ d[3] = 54/11 }}} km
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The distance left for both to go on the 
motorbike to B is:
{{{ 60 - 6 - 54/11 = 54 - 54/11 }}}
{{{ 594/11 - 54/11 = 540/11 }}} km
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{{{ 540/11 = 50*t[3] }}}
{{{ t[3] = 540/550 }}} hrs
{{{ t[3] = 54/55 }}} hrs
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{{{ t[1] + t[2] + t[3] = 6/5 + 54/55 + 54/55 }}}
{{{ t[1] + t[2] + t[3] = 66/55 + 108/55 }}}
{{{ t[1] + t[2] + t[3] = 174/55 }}}
{{{ t[1] + t[2] + t[3] = 3 + 9/55 }}}
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It looks like they can't get from A to B in under 3 hrs
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check:
{{{ d[1] + 54 - d[2] + 540/11 = 60 }}}
{{{ 6 + 54/11 + 540/11 = 60 }}}
{{{ 66/11 + 594/11 = 60 }}} 
{{{ 660/11 = 60 }}}
{{{ 60 = 60 }}}
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Hope I got it