Video Transcript
Henry is climbing a mountain which has a peak altitude of eight kilometers.
When Henry is at an altitude of two kilometers, the temperature is seven degrees Celsius.
When he is at an altitude of four kilometers, the temperature is negative five degrees Celsius.
If for every three kilometers increase in altitude, the temperature decreases by 𝑘 degrees Celsius, where 𝑘 is constant, what is the value of 𝑘?
So if we take a look at the information that we get from the question, we’re told that at two kilometers the temperature is seven degrees Celsius and at four kilometers, the temperature is negative five degrees Celsius.
So if we take a look at what’s happening here, we can see that as we increase by two kilometers, from two kilometers to four kilometers, so we’re climbing the mountain, then the temperature is decreasing by 12 degrees Celsius cause it goes from seven degrees Celsius to negative five degrees Celsius.
And if we take a look at this number line, we can see why it’s negative 12 degrees Celsius.
And that’s because if we start on seven and we’ll go to zero, that’s negative seven because we’ve taken seven away.
And if we go from zero to negative five, we’re gonna take another five away.
And if we have negative seven, take another five, we get negative 12.
So as the question talks about a decrease in temperature, we can say that two kilometers increase in altitude gives us a 12 degrees Celsius decrease in temperature.
And as we say that’s because we subtracted 12 from seven to get to negative five when we looked at the temperature decrease.
So now we want to work out how much one-kilometer increase would give us as a decrease in temperature.
And the reason we want to do that is because we’re told that 𝑘 is constant.
So we’re told that the temperature decrease is constant as we increase the altitude.
So therefore, if we find out how much the temperature decreases for one-kilometer increase in altitude, we will be able to then go and work out how much it would decrease for three kilometers increase in altitude.
So if you divide two by two, we’re gonna get one, so one kilometer.
And if we divide 12 by two, we get six degrees Celsius.
So we now know that for every kilometer Henry increases in altitude, then the temperature is gonna decrease by six degrees Celsius.
So now what we want to do is work out how much temperature would decrease if the altitude is increased by three kilometers.
And to find that, what we do is multiply each side by three.
So we get three kilometers will give us an 18-degree Celsius decrease in temperature.
So therefore, we can say that if Henry is climbing a mountain that has a peak altitude of eight kilometers.
And when he’s at an altitude of two kilometers, the temperature is seven degrees Celsius.
And then when he’s at an altitude of four kilometers, the temperature is negative five degrees Celsius.
Then, for every three-kilometer increase in altitude, the temperature decrease will be 18 degrees Celsius.
So therefore, the value of 𝑘 is going to be 18.
