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.
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
$$s_2=v\cdot t_2 = \frac{30}{T}$$
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.
Lets say he takes 100 minutes to cut the entire lawn. In 30 minutes he cuts 30%.
