On A Collision Course

In this puzzle we challenge you to figure out how close the two missiles below would be one minute before collision.

Two missiles are 41,620 km (25,860 mi) apart aimed directly at each other. One is traveling at 38,000 km/h (23,600 mph). The other is going 22,000 km/h (13,700 mph).

How far apart are they one minute before the collision? You should be able to figure this out without pencil, paper, or a calculator.

Missile

(Hint: We've given you some unnecessary information.)

Course:

Math [1]
Algebra [2]

Result/Solution(s)

Solution: On a Collision Course Math Puzzle

One minute before they collide, the missiles will be 1,000 km apart. The missile on the left is traveling at a speed of 38,000 km/h, while the one on the right is going at 22,000 km/h. Their relative speed is 60,000 km/h. Since there are 60 minutes in an hour, the speed is 1,000 km/m; so one minute before they collide, they must be 1,000 km apart. We deliberately used round numbers to make it easier to do a mental calculation.

The unnecessary information we gave was that the two missiles were 41,620 km apart at the start. All you need to do to solve the problem is to run the world backward from the moment of the crash. At 1,000 km/m, running in reverse will put the missiles 1,000 km apart one minute before the collision.