Question
On a mountain, the temperature decreases by 6.5 °C for every 1000 metres increase in height.
At 2000 metres the temperature is 10 °C.
Find the temperature at 6000 metres.
▶️Answer/Explanation
To find the temperature at 6000 meters, we can use the given information about the temperature decrease per 1000 meters.
At 2000 meters, the temperature is 10°C. From there, for every 1000 meters increase in height, the temperature decreases by 6.5°C.
To calculate the temperature at 6000 meters, we need to determine the number of 1000-meter intervals from 2000 meters to 6000 meters. Since it’s a 4000-meter increase, there are 4 intervals of 1000 meters each.
Therefore, for each interval, the temperature decreases by 6.5°C. So, over four intervals, the temperature will decrease by 6.5°C multiplied by 4, which is 26°C.
Starting from 10°C, with a decrease of 26°C, we can calculate the temperature at 6000 meters:
10°C – 26°C = -16°C
Therefore, at 6000 meters, the temperature is -16°C.
Question
The temperature at the top of a mountain is –12°C.
The temperature at the bottom of the mountain is 18°C.
(a) Work out the difference in these temperatures.
(b) 18°C is given correct to the nearest degree.
Write down the upper bound for this temperature.
▶️Answer/Explanation
(a)To calculate the difference in temperatures between -12°C and 18°C, we subtract the lower temperature from the higher temperature.
Difference = Higher Temperature – Lower Temperature
Difference = 18°C – (-12°C)
Difference = 18°C + 12°C
Difference = 30°C
Therefore, the difference in temperatures between -12°C and 18°C is 30°C.
(b) The given temperature at the bottom of the mountain is 18°C, correct to the nearest degree. To determine the upper bound, we consider the rounding convention. Since 18°C is rounded to the nearest degree, the upper bound would be half a degree above 18°C.
Therefore, the upper bound for the temperature at the bottom of the mountain is 18.5°C.
Question
One January day in Munich, the temperature at noon was 3°C.
At midnight the temperature was –8°C.
Write down the difference between these two temperatures.
▶️Answer/Explanation
To find the difference between the temperatures, we subtract the temperature at midnight from the temperature at noon:
Difference = 3°C – (-8°C)
Difference = 3°C + 8°C
Difference = 11°C
Therefore, the difference between the temperatures at noon and midnight in Munich is 11°C.
Question
At midnight the temperature in Newtown was –8°C.
At noon the next day the temperature in Newtown was 9°C.
Work out the rise in temperature from midnight to noon.
▶️Answer/Explanation
To find the rise in temperature from midnight to noon, we subtract the temperature at midnight from the temperature at noon:
Rise in temperature = 9°C – (-8°C)
Rise in temperature = 9°C + 8°C
Rise in temperature = 17°C
Therefore, the rise in temperature from midnight to noon in Newtown is 17°C.
Question
The temperature in Berlin is –7°C and the temperature in Istanbul is –3°C.
(a) Write down how many degrees colder it is in Berlin than it is in Istanbul.
(b) Sydney is 23 degrees warmer than Berlin.
Write down the temperature in Sydney.
▶️Answer/Explanation
(a) To find how many degrees colder it is in Berlin than it is in Istanbul, we subtract the temperature in Istanbul from the temperature in Berlin:
Difference = Berlin temperature – Istanbul temperature
Difference = (-7°C) – (-3°C)
Difference = -7°C + 3°C
Difference = -4°C
Therefore, it is 4 degrees colder in Berlin than it is in Istanbul.
(b) Given that Sydney is 23 degrees warmer than Berlin, we add 23 degrees to the temperature in Berlin:
Sydney temperature = Berlin temperature + 23°C
Sydney temperature = (-7°C) + 23°C
Sydney temperature = 16°C
Therefore, the temperature in Sydney is 16°C.