You can use weighted averages to solve uniform motion problems when the objects you are considering are moving at constant rates or speeds.

Suppose two cars, Car A and Car B, are moving towards one another. If the cars start 500 miles apart and Car A travels at 60 mph East and Car B travels at 65 mph West, where will the cars meet?

In order to solve this problem write an expression for the distance that each car will travel.

Next, set the sum of the distances each car travels equal to the total distance between them.

Now you can solve for the time it will take the cars to meet.

Simplify and solve for time, t.

It will take 4 hours for the cars to meet.

Now that we know how long it will take before each car meets, we can calculate the distance that each car will travel, using the distance equations from before.

Car A travels 240 miles East

Car B travels 260 miles West

Now we can conclude that the cars will meet when Car A travels 240 miles East and Car B travels 260 miles West.