Thread: Percentage Faster?

Assume I do something in 20 seconds, and that is 1.25 times faster than normal. How would I find the normal time? Also, if 20 seconds is the normal time and I need to find out what 1.25 times faster would be. Thanks!

If you run a race "twice as fast" as before that means you did it in half the time, right? If you run that race one third as fast it will take you three times as long. Note the inverse relationship - you divide the original time by the "times faster" factor. By this logic doing something in 25 seconds, and then doing it again 1.25 times faster means you did it in 25/1.25 = 20 seconds.

All times will be in seconds.
Translate "I do something in 20 seconds, and that is 1.25 times faster than normal".
Let n be the normal time it takes.
Then 20 is 1.25 times faster than n.
Thus 20 = 1.25n. Now solve for n.

There's an easy confusion, which is more about the English language than about math, as to the meaning of "1.25 times faster". If I'm going at 12 miles per hour, does "1.25 times faster" mean 1.25 times my speed, or faster by 1.25 times my speed. Does it mean 25% faster or 125% faster? Is it 12(1.25) = 15 miles per hour, or is it 12 + 12(1.25) = 27 miles per hour? You have to read it carefully, but I believe what's intended in this case is the former (even though I think technically it's the latter.)