Question 1054014
What is the tortoise's head start in miles?
Note that 12 to 3 PM is {{{ 3 }}} hrs
{{{ d[1] = ( 3/2 )*3 }}}
{{{ d[1] = 9/2 }}} mi
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Start a stop watch when the hare leaves.
Let {{{ t }}} = time on the stop watch in hrs
Let {{{ d }}} = distance in miles the hare travels
until it catches up with the tortoise.
Stop the stop watch when hare catches up
with tortoise
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The tortoise's equation:
(1) {{{ d - 9/2 = (3/2)*t }}}
The hare's equation:
(2) {{{ d = ( 15/4 )*t }}}
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Substitute (2) into (1)
(1) {{{ ( 15/4 )*t - 9/2 = (3/2)*t }}}
Multiply both sides by {{{ 4 }}}
(1) {{{ 15t - 18 = 6t }}}
(1) {{{ 9t = 18 }}}
(1) {{{ t = 2 }}} hrs
The hare catches up with the tortoise
at 3 PM plus 2 hrs = 5 PM
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(2) {{{ d = ( 15/4 )*t }}}
(2) {{{ d = ( 15/4 )*2 }}}
(2) {{{ d = 15/2 }}}
They are 7.5 miles from their starting
point when they meet
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check answer:
(1) {{{ d - 9/2 = (3/2)*t }}}
(1) {{{ 15/2 - 9/2 = (3/2)*2 }}}
(1) {{{ 6/2 = 6/2 }}}
OK