A hare & a tortoise participated in a race of 21 kilometers. Average

Question

Source: e-GMAT

A hare & a tortoise participated in a race of 21 kilometers. Average speed of hare was 6 km/per, while that of tortoise was 3 km/hr. After every 45 minutes of running, hare took rest. Hare’s first break was of 45 minutes. Every successive break was 15 minutes more than the previous break.

Select 'Winner wins by hours', & 'Winner wins by kilometer', per the information provided. Make only two selections, one in each column.

zhanbo · Accepted Answer

My answer:
'Winner win by hours'   1 Hour 
"Winner win by kilometers”  3km

The definition for two "winner win by" are not inherently consistent: They are measured at different time point. But we can figure it out.

Because Hare's speed is double that of tortoise, but Hare requires 45-minute after 45-minute race, tortoise and Hare are at the same distance from starting point after 90 minutes. After that, thanks to the Hare's incrementally lengthened rest time, Tortoise gain more and more advantage. We can generally believe that Tortoise will win even if we are unfamiliar with the famed story of the race.

So, tortoise shall complete the race at 21/3 = 7 hours. 
Let's see how much distance can Hare run within 7 hours. 
45, 45; 45, 60; 45, 75; 45 90; 45, 105...
At the end of 7 hours, Hare is at minute 60 of its 90-minute rest time. 
 45, 45; 45, 60; 45, 75; 45 9 0; 45, 105...
Totally running time 45/60*4=3 Hours
Distance: 3 X 6 = 18 km.
Because 21-18=3,
"Winner win by kilometers”  3km

In order to calculate "winner win by hours", Hare has to complete the remaining 3km. For Hare, it will take 3/6=0.5 hours
Hare is at minute 60 of its 90-minute rest time. It will then (1) Rest for another 0.5 hours (2) Run 0.5 hours to complete the race. 
For a total of 0.5 + 0.5 = 1 hour extra time. 
'Winner win by hours'   1 Hour

Sr1994 · Answer

S = D/T
   Hare

1st 45 mins 
D = T*S = 45/60 * 6 = 4.5kms
Remaining = 21 - 4.5 = 16.5 kms
Break time = 45mins
Total time = 45+45 = 90mins

2nd 45 mins 
Distance covered = 4.5kms
Remaining = 16.5 - 4.5 = 12kms
Break time = 45+15 = 60 mins (Every successive break was 15 minutes more than the previous break)
Total time = 45 + 60 = 105 mins

3rd 45 mins 
Distance covered = 4.5kms
Remaining = 12 - 4.5 = 7.5kms
Break time = 60+15 = 75mins
Total time = 45+75 = 120 mins

4th 45 mins 
Distance covered = 4.5kms
Remaining = 7.5 - 4.5 =3kms
Break time = 75+15 = 90
Total time = 90+45 = 135mins

Last stretch 
No break needed.
S = D/T
D = 3kms
S = 6km/h
T = 3/6 = 1/2 = 30mins

Total time taken for hare to complete the race = 90+105+120+135+30 = 480 => 480/60 =  8hrs

Tortoise

Since Tortoise does not rest, we can calculate the time taken for the Tortoise to complete the race directly.

S=D/T
D = 21kms
S = 3km/hr
T =  \frac{D}{S}  =  \frac{21}{3}  =  7hrs

Winner win by hours = 1hr   (total time hare took - total time tortoise took => 8-7 =1hr)
  Winner win by kilometre = 3kms   (Hare was resting before the last stretch when tortoise completed the race in 7 hrs)

Sajjad1994 · Answer

Competition mode is off now.

OA is:

'Winner win by hours':  1
 'Winner win by kilometer':  3

steck · Answer

I get the same result as  zhanbo

Pragun1710 · Answer

how are we supposed to do this under 3 minutes?

A hare & a tortoise participated in a race of 21 kilometers. Average

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'Winner win by hours'	'Winner win by kilometer'
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GMAT Two-part Analysis (TPA) Questions

A hare & a tortoise participated in a race of 21 kilometers. Average

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