How to solve uniform motion problems using distance, rate, and time
When an object moves at a constant speed, we can find the distance by multiplying speed by elapsed time. If there are two travelers, it helps to write one equation for each. Let’s see how a shared distance connects the two equations.
Match the units in the distance formula
If the rate is in miles per hour, measure elapsed time in hours and distance in miles. Choose a variable for the unknown and use the story to tell which distances or times are related.
Example: Two trains travel the same route
The first train takes eight hours. The second takes ten hours at 40 miles per hour. Both travel from the same starting station to the same destination along the same route, so they cover the same distance.
The first train travels at 50 miles per hour.
Example: One driver starts four hours later
Cassie drives at 30 miles per hour. Four hours later, Susan leaves the same point at 60 miles per hour. Let be Cassie’s driving time when Susan catches up. Susan has driven for hours.
Cassie drives eight hours and Susan drives four. They each travel miles, since .
Apply the same idea to the video example
Arnold drives at 12 miles per hour, and Kay drives the same route at 20 miles per hour in two fewer hours. If Arnold takes hours, equate and . This gives , so the distance is miles.
