Question: Mount Kinabalu is $4095$ m high. The temperature is $23°$C at the foot and $-5°$C at the top, decreasing at a constant rate with height. Find (a) the temperature at a height of $2340$ m, (b) the height at which the temperature is $7.5°$C.

Step 1. Pin down the rate — total change over total height:

$$\text{Temperature drop} = 23 - (-5) = 28°\text{C over } 4095 \text{ m}$$

Step 2. (a) The drop over $2340$ m is the matching fraction of $28°$C:

$$\text{Drop} = \dfrac{2340}{4095} \times 28 = \dfrac{4}{7} \times 28 = 16°\text{C}$$

Step 3. Subtract from the foot temperature:

$$23 - 16 = 7°\text{C}$$

Step 4. (b) Work backwards: a temperature of $7.5°$C is a drop of $23 - 7.5 = 15.5°$C, so

$$\text{Height} = \dfrac{15.5}{28} \times 4095 = 2266.875 \text{ m} \approx 2270 \text{ m}$$

⚠ Watch out: The total change is $23 - (-5) = 28$, not $18$ — subtracting a negative adds. Rates work in both directions (height → temperature, temperature → height); each part starts from the change, never from the raw reading.