Question

In drilling world's deepest hole it was found that the temperature T in degree celcius, x km below the earth's surface was given by T = 30 + 2.5 (x -3), 3 $\le x\le 15$. It was assumed that this drilling resulted

$5\%$ increase in carbon dioxide level at a temperature above

${205}^{\circ }$ and below ${155}^{\circ }C$, so drillers tried to control the depth between these two limits. At what depth will the temperature be between ${155}^{\circ }$ and ${205}^{\circ }$ What values are depicted here by the drillers for selecting this temperature range ?

Answer 1

We have, T = $30+25(x-3),3\le x\le 15$

Now, T lies between 155${}^{\circ }$ and ${205}^{\circ }$C

$\therefore$ 155 < T < 205

$\Rightarrow$ 155 < 30 + 25 (x-3) < 205 [from Eq. (i)]

$\Rightarrow$ 155 - 30 < 30 + 25 (x - 3)- 30 < 205 - 30

$\Rightarrow$ 125 < 25 (x - 3) < 175 $\Rightarrow$

$\frac{125}{25}$ < $\frac{25(x-3)}{25}$ < $\frac{175}{25}$

$\Rightarrow$ 5 < (x-3) < 7 $\Rightarrow$ 5 + 3 < x -3+3<7 + 3

$\Rightarrow$ 8 < x < 10

Hence, at the depth 8 to 10 km temperature lies between ${155}^{\circ }C$ to ${205}^{\circ }$C Drillers are aware towards environmental pollution because increased $C{O}_2$ concentration leads to Global warming to which results in

(i) Abnormal weather condition

(ii) Various diseases

(iii) Earthquake and Tsunami.