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 2 t square metres per minute. How long will it take him to dig an area of…

Question

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 2 t square metres per minute. How long will it take him to dig an area of 40 square metres?

Accepted Answer

Correct answer: A. (a): If x is the area of the area dug at any time t, then dx dt= 2 t ∴x=4 t+c When t=0 ,x=0 ∴c=0 ∴x=4 t When x=40 ,40=4 t ⇒ t=10 ∴ t=100 min.

$A gardener is digging a plot of land. As he gets tired, he works more slowly. After ' t' minutes he is digging at a rate of \frac{2}{t} square metres per minute. How long will it take him to dig an area of 40 square metres?$

Solution

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