Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

i doubt this is that simple

Answer 6

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

Answer 7

1253 - x?

Answer 8

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

Answer 9

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

Answer 10

hmm then that's not right

Answer 11

WHY???

Answer 12

like i said...it's not simple

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

because you think you're right?

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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.

Answer 21

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

Answer 22

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

Answer 23

*

:P

Answer 24

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

Answer 25

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

Answer 26

me too i dont see a mistake in the solution

Answer 27

whats the ans in the book ?

Answer 28

and speeds are already given right ?

Answer 29

ahh i think i get what the question is asking

Answer 30

I got 1128. using a much more complex method.

Answer 31

hmm maybe I can get an idea from that complex method

Answer 32

this is a headscratcher

Answer 33

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

Answer 34

so your answer is 1128 too huh

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

No. It doesn't mean that here.

Answer 40

@lgbasallote I agree with Yahoo's answer also.

Like this is the way I thought of it:



Since like everyone is saying A finished 3 seconds after T.
So that means A finished in 1253 seconds.