Richard and Gerald are walking toward each other on a straight road 10 km long. Richard travels at a rate of 3.3 km/hr, and Gerald travels at 4.2 km/hr. When they start walking, Richard’s dog Checkers runs toward Gerald at 9 km/hr, and runs back toward Richard as soon as he reaches Gerald. If Checkers continues to run back and forth between Richard and Gerald, what is the total distance in km that Checkers travels before Richard and Gerald meet each other, assuming that Checkers wastes no time turning around? Please show me the steps.

Question

Richard and Gerald are walking toward each other on a straight road 10 km long.  Richard travels at a rate of 3.3 km/hr, and Gerald travels at 4.2 km/hr.  When they start walking, Richard’s dog Checkers runs toward Gerald at 9 km/hr, and runs back toward Richard as soon as he reaches Gerald.  If Checkers continues to run back and forth between Richard and Gerald, what is the total distance in km that Checkers travels before Richard and Gerald meet each other, assuming that Checkers wastes no time turning around?  Please show me the steps.