I looked up these three words in Oxford Dictionary and I found that they seem to be interchangeable in some cases.
Here's the question: what's the difference between the three words?
Rate: [countable] a measurement of the speed at which something happens.
Most people walk at an average rate of 5 kilometres an hour. At the rate you work, you'll never finish!
Pace: [singular, uncountable] the speed at which something happens.
It is difficult to keep up with the rapid pace of change. We encourage all students to work at their own pace (= as fast or as slow as they can).
Speed: 1 [countable, uncountable] the rate at which somebody/something moves or travels.
He reduced speed and turned sharp left.
Speed 2 [countable, uncountable] the rate at which something happens or is done.
This course is designed so that students can progress at their own speed.
Speed: 3. [uncountable] the quality of being quick or rapid
The train began to pick up speed (= go faster). Increasing your walking speed will help to exercise your heart.
The accident was due to excessive speed. Speed is his greatest asset as a tennis player.
Tempo: the speed of any movement or activity
the increasing tempo of life in Western society
Don’t let the other team dictate the tempo of the game
Best Answer
Those 4 words above-mentioned are sometimes used interchangeably, but there are some clear distinctions.
Pace originally meant:
[Online Etymology Dictionary]
Therefore, you use "pace" in place of speed to describe something slow and steady.
For example, you use a "pace-maker" in stead of "speed-maker" for your heart device or someone who sets the pace in a race such as marathon as it means:
[Oxford Online Dictionary]
However, if you describe a car or an airplane, you don't use "pace" for its "speed".
Tempo originally meant:
[Online Etymology Dictionary]
You also use "tempo" in place of speed to describe something slow and steady as it means:
[Oxford Online Dictionary]
Rate originally meant:
[Online Etymology Dictionary]
Rate is often used for "frequency" or "quantity".
It can also mean:
[Oxford Online Dictionary]
You use "economic growth rate" not "economic growth speed" when it is expressed in a percentage.