simple algebra 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

Question

simple algebra 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

goldphenoix · Answer

I think I can solve it. 1km = 1000m?

anonymous · Answer

yes. i think so

rsadhvika · Answer

18.8 minutes

anonymous · Answer

any solutions to prove?

goldphenoix · Answer

I will be assuming that 1km = 1000m.
So, halfway through the track, Achilles took a nap.
Halfway through the track is 5km or 500m. 
It took Achilles about 62.5s, or 1 minute and 2.5 seconds.

Hmm. So he lost to the tortoise by 3 seconds. So tortoise won by 3 second, with a speed of
0.8m/s.  

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goldphenoix · Answer

Harder than I thought...

anonymous · Answer

indeed it is :)

rsadhvika · Answer

tortoise time : 1000/.8 = 1250
achilles time : 1253

achilles sleep = 1253 - 1000/8

rsadhvika · Answer

that gives 18.8 minutes.. just a short nap lol

goldphenoix · Answer

"achilles time : 1253"? 
How did you get that?