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Question

Searches related to as an airplane rises, the outside temperature drops 3.6F for each 1000 feet of elevation gain. suppose the outside temperature is 65f on the ground when the plane takes off and 43f at cruising altitude. how high is the plane then

Answer 1

In order to work this out, the first thing to figure out is how much the temperature actually changed, since the elevation is tied directly to that.

On the ground it was 65 degrees and at cruising altitude it was 43 degrees, so:

65 - 43 = 22

The temperature dropped 22 degrees total.

Now we use the rate we were given. It drops 3.6 degrees for every 1000 feet, so the question becomes how many groups of 3.6 degrees fit inside 22 degrees. That is a division:

22 / 3.6 = 6.111...

Remember what that number actually means, because this is the step people usually miss. It is not feet. It is how many 1000-foot chunks the plane climbed. To get the answer in feet we multiply by 1000:

6.111 x 1000 = 6111 feet

If setting up a proportion feels more natural to you, that works too. Match degrees to feet on both sides:

3.6/1000 = 22/x

Cross multiplying gives 3.6x = 22000, and dividing by 3.6 gives x = 6111, the same answer.

So, our final answer is that the plane is at about 6,111 feet.

Answer 2

The temperature change is 65 - 43 or 22°F

Since the temperature drops 3.7°F for each 1000 feet, we just need to know how many "3.7's" there are in 22. We find that out by dividing.

So 22/3.7 = 5.946

That means the altitude must be at 5.946•1000 ft or 5,946 feet above the altitude it took off at.

It might be easier to think about if you made a simple version of this problem up. What if there temperature dropped by 15°F and what if the temperature changes by 5°F for each 1000 feet. Can you see that the altitude must be 3000 feet (the temp drops 5°F after 1000 ft, then another 5°F in the second 1000 ft and then another 5°F in the third 1000 ft)? So we take the temperature change (15°F) divided by the rate the temperature changes (5°F/1000ft) then multiply by 1000 (15/5 = 3 and 3•1000 = 3000 ft. We do the same with the real problem: 22°F/3.7°F = 5.946 and 5.946•1000 = 5946 ft