## lgbasallote Group Title 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 one year ago one year ago

1. Yahoo! Group Title

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

2. lgbasallote Group Title

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

3. lgbasallote Group Title

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

4. Yahoo! Group Title

$S=\frac{ d }{ t }$

5. lgbasallote Group Title

i doubt this is that simple

6. sauravshakya Group Title

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

7. lgbasallote Group Title

1253 - x?

8. lgbasallote Group Title

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

9. sauravshakya Group Title

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

10. lgbasallote Group Title

hmm then that's not right

11. sauravshakya Group Title

WHY???

12. lgbasallote Group Title

like i said...it's not simple

13. lgbasallote Group Title

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

14. Yahoo! Group Title

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

15. lgbasallote Group Title

16. lgbasallote Group Title

because you think you're right?

17. Yahoo! Group Title

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

18. lgbasallote Group Title

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

19. lgbasallote Group Title

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

20. myininaya Group Title

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.

21. myininaya Group Title

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

22. myininaya Group Title

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

23. shubhamsrg Group Title

* :P

24. shubhamsrg Group Title

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

25. lgbasallote Group Title

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

26. ganeshie8 Group Title

me too i dont see a mistake in the solution

27. shubhamsrg Group Title

whats the ans in the book ?

28. shubhamsrg Group Title

and speeds are already given right ?

29. lgbasallote Group Title

ahh i think i get what the question is asking

30. alexyn Group Title

I got 1128. using a much more complex method.

31. lgbasallote Group Title

hmm maybe I can get an idea from that complex method

32. lgbasallote Group Title

33. alexyn Group Title

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

34. lgbasallote Group Title

35. alexyn Group Title

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

36. lgbasallote Group Title

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

37. alexyn Group Title

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

38. lgbasallote Group Title

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

39. alexyn Group Title

No. It doesn't mean that here.

40. myininaya Group Title

@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.

41. myininaya Group Title

125/2+nap+125/2 =1253

42. myininaya Group Title

125+nap=1253

43. lgbasallote Group Title