# How many meters does Johnson beat Chris by?

Johnson, James, and Chris race each other in a 100 meters race.

All of them run at a constant speed throughout the race.

Johnson beats James by 20 meters.

James beats Chris by 20 meters.

How many meters does Johnson beat Chris by?

It is tempting to guess that Johnson beats Chris by 40 meters, but when Johnson finishes and is 20 meters ahead of James, James is NOT 20 meters ahead of Chris (he’s only 16 meters ahead), and it will take a couple more seconds before James increases his lead over Chris to 20 meters.

To figure out the answer, we let Johnson’s speed be X meter/second. So it takes him 100/X seconds to finish the race.

At this point, we know that James has run 80 meters (since Johnson beats him by 20 meters).

So James runs 80 meters in 100/X seconds, meaning that he is running at a speed of (80/(100/X)) meters/second, or (8X/10) meters per second.

So we then know that it takes James 100/(8X/10) seconds to finish the race, or 125/X seconds.

At this point, we know that Chris has run 80 meters (since James beats him by 20 meters).

So Chris runs 80 meters in 125/X seconds, meaning that he is running at a speed of (80/(125/X)) meters/second, or 80X/125 meters per second.

Now that we know Chris’s speed, we just need to figure out how far he had run when Johnson finished the race.

Since Johnson finished in 100/X seconds, we can determine that Chris had run;

(100/X) * (80X/125) = 8000/125 = 64 meters;

when Johnson finished the race.

And so Johnson beat him by (100 – 64) = 36 meters.