Question 1054159
9:25 minus 9:00 = 25 min
25 min = {{{  25/60 }}} hrs
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What is your friend's head start in miles?
{{{ d[1] = 2*(25/60) }}}
{{{ d[1] = 5/6  }}} mi
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Start a stopwatch when you start hiking and
stop it when you catch up with friends
Let {{{ t }}} = time on stopwatch in hrs
Let {{{ d }}} = distance in miles you travel
until you catch up with friends
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Your equation:
(1) {{{ d = 3t }}}
Friend's equation:
(2) {{{ d - 5/6 = 2t }}}
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Plug (1) into (2)
(2) {{{ 3t - 5/6 = 2t }}}
(2) {{{ t = 5/6 }}}
and
(1) {{{ d = 3*(5/6) }}}
(1) {{{ d = 5/2 }}}
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(a)
You hike 2.5 mi until you catch up with friends
(b)
{{{ 5/6 = 50/60 }}} hrs
9:25 + 50 min = 10:15
You catch up with friends at 10:15
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check:
Your friends should cover {{{ 2.5 }}} mi in 25 min plus 50 min
= 75 min which is 1.25 hrs
{{{ d = 2*1.25 }}}
{{{ d = 2.5 }}} mi
OK