Achilles and a tortoise were racing on a 1 km track. Achilles runs on a constant 8 m/s speed and the tortoise's speed is 0.8 m/s. Halfway through the track, Achilles decided to take a nap since the tortoise was so far behind. However, when he woke up, the tortoise was already near the finish line. Achilles started to run again with constant speed of 8 m/s, but he lost to the tortoise by 3 seconds. How long did Achilles sleep?
Note: Let the tortoise and Achilles' speed be constant

- lgbasallote

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- anonymous

T(torto) = 625 + 625 = 1250s to Cover 1000m
T(achilles) = 62.5 + 62.5 = 125s to cover 1000m
Since the Achilles reached 3 Seconds Later
.it lost by 3 seconds means
125 + x = 1253
x = 1128s

- lgbasallote

i don't think that's right.....

- lgbasallote

what's that 625 on the first line by the way?

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## More answers

- anonymous

\[S=\frac{ d }{ t }\]

- lgbasallote

i doubt this is that simple

- anonymous

8(1253-x)=1000
x=1128 seconds
Looks correct to me.

- lgbasallote

1253 - x?

- lgbasallote

you do know i asked how long Achilles slept and not how long Achilles was running...right?

- anonymous

x is the time for which Achilles sleeps......
So, 1253-x gives how long he ran.

- lgbasallote

hmm then that's not right

- anonymous

WHY???

- lgbasallote

like i said...it's not simple

- lgbasallote

the question is...what's the right solution...

- anonymous

@lgbasallote which part Do u think...i made a Mistake...

- lgbasallote

why are you asking me? i'm the asker here...you tell me....

- lgbasallote

because you think you're right?

- anonymous

Toto took 1250s To cover 1000m.... right.?

- lgbasallote

no need to explain to me your solution..i get it

- lgbasallote

..it's the book that says it's wrong..not me

- myininaya

Did he shout?
You guys play nice please.
People can disagree with answers. I don't find it rude to do so.
I'm not saying anyone's answer is right here. I'm just saying people have a right to disagree but please be respectful about it.

- myininaya

I will be deleting anything I find nasty here. Thanks.

- myininaya

Keep in mind. Discussion is an awesome tool in learning. :)

- shubhamsrg

*
:P

- shubhamsrg

though no one asked,,but i guess yahoo is right..

- lgbasallote

i suppose one needs to get the speeds first...

- ganeshie8

me too i dont see a mistake in the solution

- shubhamsrg

whats the ans in the book ?

- shubhamsrg

and speeds are already given right ?

- lgbasallote

ahh i think i get what the question is asking

- anonymous

I got 1128. using a much more complex method.

- lgbasallote

hmm maybe I can get an idea from that complex method

- lgbasallote

this is a headscratcher

- anonymous

Alright. Using your head. visualize the problem. A 1000 meter track. Tortoise and Achilles begin running. Achilles pulls ahead and half way takes a nap. Thats after 62.5 seconds. He's already covered 500 m. At that same time Achilles sleeps, Tortoise has reached 50 m. Now using that knowledge, we know it will take the Tortoise 1187.5 s to finish. It'll take Achilles 62.5 s. So subtract Achilles time from Tortoise's. Which gives you. 1,187.5 s - 62.5 = 1,125 s. Add three seconds. = 1,128 s

- lgbasallote

so your answer is 1128 too huh

- anonymous

Yep. It makes complete sense. He napped for 1,128 seconds. in order to finish 3 seconds after tortoise.

- lgbasallote

what if the 3 seconds doesn't mean that Achilles finished 3 seconds later?

- anonymous

Oh it does. Because at 1,125 s. Achilles finished right with tortoise. But adding 3 seconds means he finished 3 seconds later.

- lgbasallote

i meant 3 seconds can mean that Achilles' running time is 3 more than the tortoise's

- anonymous

No. It doesn't mean that here.

- myininaya

@lgbasallote I agree with Yahoo's answer also.
Like this is the way I thought of it:
|dw:1350569105212:dw|
Since like everyone is saying A finished 3 seconds after T.
So that means A finished in 1253 seconds.

- myininaya

125/2+nap+125/2 =1253

- myininaya

125+nap=1253

- lgbasallote

hmm i'll think about this. this is supposedly a tricky question

- ganeshie8

this is tricky only.. i see it now only :)
answer must be : 1250 - (62.5+3)
bit ambiguous... but okay... ..

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