KCET · Maths · Functions
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?
- A \( 10 \) minutes
- B \( 40 \) minutes
- C \( 100 \) minutes
- D \( 30 \) minutes
Answer & Solution
Correct Answer
(C) \( 100 \) minutes
Step-by-step Solution
Detailed explanation
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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