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 miles per hour (mph), while the tortoise could pedal only at a rate of 12mph. Knowing he was slower, the tortoise makes up a lame excuse for being given a 27-mile head start in the 165-mile race.
What is the largest head start the tortoise could have been given without being able to beat the hare? Explain.
2007-11-09 03:01:39 · 7 answers · asked by . 1 in Science & Mathematics ➔ Mathematics
The time it took for the hare to bicycle to the finish line was:
165 mi * (1hr/15mi) = 11 hrs
In 11 hrs the tortoise travels
12 mi/1hr * 11hr = 132 mi
So to tie with the hare, the tortoise needs a head start of
165-132 = 33 mi
The answer is 33mi EXACTLY. With a head start of 33mi, it's a tie, which means the tortoise still hasn't beaten the hare.
2007-11-09 03:26:27 · answer #1 · answered by DWRead 7 · 2⤊ 0⤋
Time for hare to finish race:
165/15 = 11 hrs
Time for tortoise to finish race (if it were to start from the start):
165/12 = 13.75 hrs
For the tortoise and the hare to tie, they would both have to be able to finish the race in 11 hours.
Therefore, headstart of tortoise = 2.75 hrs
= 2.75 * 12 = 33 miles.
Therefore, if the tortoise had a 33 mile head start, the hare and the tortoise would tie.
Therefore the largest head start the tortoise could have without being able to beat the hare is 32.999 recurring miles.
Hope that helps :)
2007-11-09 11:13:03 · answer #2 · answered by Micoaw 3 · 0⤊ 0⤋
Calculate the time it takes for the hare to finish the race (165/15).
Calculate how far the tortoise can pedal in that time (12*165/15).
Subtract that answer from 165. That is the maximum head start for a tie. Anything less than that and the hare wins.
2007-11-09 11:10:28 · answer #3 · answered by T 5 · 0⤊ 0⤋
the hare ran the race in 11 hours( 165/15). so, the tortoise runs 132 miles in those 11 hours(12 x 11), so if the tortoise gets a 33 mile head start(165 - 132), they tie. EDIT - the answer IS 33, tying is not beating .
2007-11-09 11:09:15 · answer #4 · answered by bsxfn 3 · 0⤊ 0⤋
33 mile head start would produce a tie, so anything less than that. 165Mile race minus the head start of 33 miles equals 132 total miles. Divided by 12mph, is 11. The number of hours it will take to finish. The hare will finish in 11hours at a rate of 15mph.
2007-11-09 11:23:27 · answer #5 · answered by jtrd39 1 · 0⤊ 0⤋
Hi,
Write the rate*time=distance for both the hare and tortoise.
Hare:
15t = 165
t=165/15
=11
Tortoise:
12t + s = 165....(Where s = heat start distance.)
12(11) +s = 165.....(Remember that the times are the same.)
132 +s = 165
s=165-132
s = 33 miles
Any more head start and the tortoise wil win.
FE
2007-11-09 11:53:34 · answer #6 · answered by formeng 6 · 0⤊ 0⤋
dude above me didnt answer the question properly
2007-11-09 11:10:06 · answer #7 · answered by Sceptic 1 · 1⤊ 3⤋