Question

Could someone please help me with this question?
http://i.imgur.com/jThn7Lu.jpg

Answer 1

Distance travelled = speed * time
60 minutes in one hour

s by tortoise = 5.4 * 60 = 324
s by hare = 19.2*10 + 0*30 + 19.2*10 + 0*20 = 384

Answer 2

@kamalkayani Thanks, but I already had the answer to that. I was looking for B.

Answer 3

for part b)
time taken by tortoise:
\[={1000\over5.4}=185\,{\rm min}\]
in that time, the hare performs "5" hops and the distance travelled:
\[
=19.2\times5\times10=960\,{\rm m}
\]
so, the difference between the two distances:
\[1000-960=40\,{\rm m}\]

Answer 4

C)
for the hare to win, we have to find the speed:
\[
s={1000\over 5\times10}=20\,{\rm m/min}
\]

Answer 5

@electrokid Could you please also help me with D?

Answer 6

D)
lets say after distance "d" and time "t", the hare catches up with the tortoise. the time for this to happen is the same
\[
d_t=5.4t
\]
in this time, the hare performs "n" hops (say)
\[
d_h=192n
\]
we want
\[d_h>d_t\\
192n>5.4t\\
{192\over5.4}>{t\over n}\\
35.6>{t\over n}
\]
this can never happen since \[{t\over n}\ge40\]
so, the hare will not be completey ahead of the tortoise

Answer 7

Are you sure @electrokid otherwise the question must've been written incorrectly.

Answer 8

no. the "D" is tricky. Not sure.

Answer 9

well, look at it
in 40min, the tortoise travels = \(40\times 5.4=216{\rm m}\)
in 40min, the hare travels = \(10\times19.2=192{\rm m}\)

so, every 40min, the tortoise gets a lead over the hare and hence, the hare will never go permanently ahead of the tortoise

This is ZENO'S PARADOX

Answer 10

@electrokid It might be a trick question... There always will be a change. Thanks.