Three stooges

Algebra Level 3

One thing you may not know about the three stooges is that they love math, even though they aren't very good at it.
It takes Moe, the smartest of the three, an hour to do this math problem.
Larry, who is not far from moe in intelligence, two hours to do this problem.
Last and least we have Curly who takes 7 hours to do this problem, bless his little heart.
How seconds does it take the three of them combined to solve this problem?
Round to the nearest second and don't round till your final answer.

The answer is 2191.

1 solution

Hung Woei Neoh
Jun 9, 2016

Now, we assume that their rate (or speed) of solving problems can be added together linearly.

We know that

$\text{Problems solved = Rate of solving problems }\times \text{ Time spent}$

Therefore,

Rate of solving problems of Moe $= \dfrac{1}{1 \times 60 \times 60}=\dfrac{1}{3600}$ problems per second

Rate of solving problems of Larry $= \dfrac{1}{2 \times 60 \times 60}=\dfrac{1}{7200}$ problems per second

Rate of solving problems of Curly $= \dfrac{1}{7 \times 60 \times 60}=\dfrac{1}{25200}$ problems per second

Combining all their effort together, their total rate of solving problems

$=\dfrac{1}{3600} + \dfrac{1}{7200} + \dfrac{1}{25200} = \dfrac{14+7+2}{50400} = \dfrac{23}{50400}$ problems per second

Therefore, the time taken for the $3$ of them to solve a problem together

$=\dfrac{1}{\left(\frac{23}{50400}\right)} = \dfrac{50400}{23} \approx \boxed{2191}$ seconds

Three stooges

The answer is 2191.

1 solution

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