Ex 1.4, 5 The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?Temperature at 12pm = 10°C
Temperature decreases at 2°C per hour
We need to find
Time when temperature is 8°C below zero, i.e., −8°C
∴ Total decrease = Final temperature − Initial Temperature
= −8°C − 10°C
= −8 − 10
= −(8 + 10)
= −18°C
Now,
Temperature decrease in 1 hour × Total number of hours
= Total decrease
Total number of hours = (𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒)/(𝑇𝑒𝑚𝑝𝑒𝑎𝑡𝑢𝑟𝑒 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 1 ℎ𝑜𝑢𝑟)
= (−18)/(−2)
= 18/2
= 9
So, in 9 hours, temperature becomes −8°C
∴ Temperature is – 8°C at 9 PM
Now,
We need to find temperature at mid-night
Temperature at 12 AM − Temperature at 12 PM
= Temperature change in 12 hours
Temperature change in 1 hour = −2°C
Temperature change in 12 hours = −2 × 12°C
= −24°C
Now,
∴ Temperature at 12 AM − Temperature at 12 PM
= Temperature change in 12 hours
Temperature at 12 AM − 10°C = −24°C
Temperature at 12 AM = −24 + 10 °C
Temperature at 12 AM = −(24 − 10) °C
Temperature at 12 AM = −14°C
∴ Temperature at mid-night = −14°C

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.