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A gardener is digging a plot of land. As he gets tired, he works more slowly. After 't' minutes he
is digging at a rate of \( \frac{2}{\sqrt{t}} \) square metres per minute. How long will it take him to dig an area of
\( 40 \) square metres?
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is digging at a rate of \( \frac{2}{\sqrt{t}} \) square metres per minute. How long will it take him to dig an area of
\( 40 \) square metres?
Solution:
1841 Upvotes
Verified Answer
The correct answer is:
\( 100 \) minutes
Given that, $\frac{d A}{d t}=\frac{2}{\sqrt{t}}$
$\Rightarrow d A=\frac{2}{\sqrt{t}} d t$
Integrating both the sides, we have
$\int d A=\int \frac{2 d t}{\sqrt{t}}$
$\Rightarrow A=2 \cdot 2 \sqrt{t}+C$
When $t=0$ we have $C=0$
So, $4 \sqrt{t}=40$
$\Rightarrow t=10^{2}=100 \mathrm{~min}$
$\Rightarrow d A=\frac{2}{\sqrt{t}} d t$
Integrating both the sides, we have
$\int d A=\int \frac{2 d t}{\sqrt{t}}$
$\Rightarrow A=2 \cdot 2 \sqrt{t}+C$
When $t=0$ we have $C=0$
So, $4 \sqrt{t}=40$
$\Rightarrow t=10^{2}=100 \mathrm{~min}$
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