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 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?

Answer 1

T = 30 + 25(x – 3), 3 ≤ x ≤ 15

Where, T = temperature and x = depth inside the earth

The Temperature should be between 155°C and 205°C.

So, we get,

⇒ 155 < T < 205

⇒ 155 < 30 + 25(x – 3) < 205

⇒ 155 < 30 + 25x – 75 < 205

⇒ 155 < 25x – 45 < 205

Adding 45 to each term, we get

⇒ 200 < 25x < 250

Dividing each term by 25, we get.

⇒ 8 < x < 10

Hence, temperature varies from 155° C to 205° C at a depth of 8 km to 10 km.