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A man can cut the grass in $T$ minutes What part of the lawn can be cut can be cut in $30$ minutes?

Options: a) $\frac{30}{T}~~~~$ b) $T-30~~~~$ c) $\frac{T}{30}~~~~$ d) $30-T$

My approach:

$1$ man can cut in $T$ minutes. therefore $\frac{T}{30}$ can be cut by $1$ man, but the answer is different. What part can be cut in $30$ minutes I am not able to think of can you explain me with an analogy.

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The correct answer is a)

His clearing speed 1/T, meaning one lawn per T minutes.
So if you multiply his cutting speed by the time used, you get the part of the lawn: $$1/T\cdot 30 =\frac{30}{T}$$

Explanation His part of lawn mown per time is constant.
This means $$\frac{\text{part of lawn mown}}{\text{time used}}= \text{cutting speed}$$ or $$\frac{s_i}{t_i} = v \quad \forall i$$ defined as the text equation above. We are given a part $s_1=1$ and $t_1 =T$, so we know $$v=\frac{1}{T}$$ And we know $t_2=30$ and want to know $s_2$.
So $$s_2=v\cdot t_2 = \frac{30}{T}$$

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Try to plug in a number. For example, let's say that $T=60$. Then, obviously, a man can cut half of the lawn in $30$ minutes, while by your guess, it the result would be $\frac{T}{30} = 2$, so by your guess, the man can cut two lawns in $30$ minutes. Obviously wrong.

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Lets say he takes 100 minutes to cut the entire lawn. In 30 minutes he cuts 30%.

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