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$10$ cats can eat $10$ mice in $20$ minutes. $2$ cats started eating $60$ mice in $3$ minutes, then another $6$ cats were added, how many more minutes will it take them to consume the remaining mice?

I got the answer as $149.25$ minutes. But it seems to be wrong. Can anyone help out?

Since it'll take too long for me type out my solution, I'll just mention the key points I got:-

Since $10$ cats can eat $10$ mice in $20$ minutes, I figured $1$ cat can eat $1$ mouse in $20$ minutes. From this, I got that $2$ cats can eat $0.3$ mice in $3$ minutes. So, the question then is, $8$ cats can eat $(60-0.3)$ mice in (?) minutes. According to my reasoning, $8$ cats can eat $1$ mouse in $2.5$ minutes. And so, I figured $8$ cats can eat $59.7$ mice in $149.25$ minutes.

Can anyone expand on where I went wrong?

Jeel Shah
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Train Heartnet
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  • Your logic & answer are correct. You can cross-check/disclose the answer if there is something wrong in the question, may be the unit – lab bhattacharjee May 19 '13 at 14:35
  • "2 cats started eating 60 mice in 3 minutes" is not clear. So 2 cats started to eat mice, there were 60 mice, what does the 3 minutes refer to? Does it mean, 6 cats were added 3 minutes later? – nycynik May 19 '13 at 15:19

1 Answers1

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Your logic seems spot on, in the sense that it's probably the sort of reasoning you are expected to do. But does that make it right?

What if we accept the basic fact that cats do not share? So though 10 cats eat 10 mice in 20 minutes, 10 cats would also eat 1 mouse in 20 minutes since one cat eats the mouse and the other cats all watch greedily (I'll make the assumption that the cats aren't boisterous, and that all time playing with the food, i.e. letting the mouse thinks it gets away before clawing it back, have been included in the 20 minutes).

Then every 20 minutes, the 8 cats will eat on average 8 mice. Rather, if we let time start at $0$, then every $20t$, 2 mice are eaten, and at every $20t + 3$, 6 mice are eaten. Going along this logic, the last mouse is eaten at $20\cdot 8 + 3 = 163$ minutes, although for the last $17$ minutes there are 2 cats eating mice and the other 6 cats are busy being incredibly fat, having eaten so many mice.

davidlowryduda
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