Traveler Problems worksheets for Grade 6 (Elementary School)

The time until two people walking toward each other meet, or until one catches up with the other from behind, is found from the sum or the difference of their speeds. Finding the meeting place or a speed in reverse, time-difference problems and catching up around a pond follow, along with average speed and distance for a trip that combines walking and running.

Dividing by the difference in a meeting problem and by the sum in a catching-up problem is the most frequent mix-up. In time-difference problems, the distance already covered by the person who set off first goes unsubtracted. Around a pond, children work from the gap between the two rather than dividing one full lap by the difference in speeds.

The idea gained in Speed in grade 5, finding speed from distance and time, is stretched here to two people moving at the same time. Working out how the distance between them changes over time is what's new in this unit. The same idea is taken up again before the grade ends, in Various Word Problems, applied to a speed version of Cranes and Turtles.