<PRE><B>Question 127785</B>
Years after the famous foot race, the hare challenged the tortoise to a rematch
 on bicycles. the hare was able to pedal at a rate of 15 MPH while the tortoise
 could only pedal at 12 mph. knowing he was slower, the tortoise made up a lame
 excuse to be given a 27 mile head start. in the 165 mile race.
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1. Who won the race? by how much time? explain
:
Can the tortoise travel (165-27) in less time than the rabbit travels 165 mi?
:
Hare&#39;s time; (Time = {{{distance/speed)}}})
{{{165/15}}} = 11 hrs
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Tortoise&#39;s time
{{{((165-27))/12}}} = 11.5 hrs
:
Obviously the hare wins by half an hour
:
: 
2. How far into the race did the hare overtake the tortoise?
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When this occurs they will have traveled for the same length of time
Time = distance/speed
:
Hare&#39;s time = Tortoise&#39;s time
Let d = distance from the starting line of the hare
{{{d/15}}} = {{{((d-27))/12}}}
Cross multiply
15(d-27) = 12d
15d - 405 = 12d
15d - 12d = +405
3d = 405
d = {{{405/3}}}
d = 135 miles into the race, the hare overtakes the tortoise
:
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3. what is the largest head start that tortoise could have been given without being able to beat the hare?
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Let x = the largest head start which will cause a tie, 
Their travel times are equal. Write a time equation:
{{{165/15}}} = {{{((165-x))/12}}}
Cross multiply:
15(165-x) = 12 * 165
2475 - 15x = 1980
2475 - 1980 = 15x
495 = 15x
x = {{{495/15}}}
x = 33 mile head start would be a tie
:
Check for equal time:
165/15 = 11 hr
132/12 = 11 hr
;
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4. suppose a chipmunk entered the race with an 84 mile head start traveling 9
 mph. develope an equation for the chipmunk and calculate when the hare would 
finally catch up to the chipmunk assuming the race does not end at 165 miles.
:
Another situation where the travel time is equal for both:
Let a = distance from start that the hare catches up with the chipmunk
{{{a/15}}} = {{{((a-84))/9}}}
Cross multiply:
15(a-84) = 9a
15a - 1260 = 9a
15a - 9a =+1260
a = {{{1260/6}}}
a = 210 miles from start for the hare to catch up with the chipmunk
:
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5. a confused pig also followed the race course. the pig started at the finish line at a rate of 15v mph traveling backwards. where and when did he meet the hare on the road?
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I&#39;m not sure if it is 15v or 15 mph, if you mean the pig travels at 15 mph as the hare. They would meet at the half way mark (Assuming they started at the same time)


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