A travel coordination system allows a rider to request a trip with a flexible departure time. The rider can specify a pick-up location, a trip destination, a target trip price, and a departure timeframe for the trip. The travel coordination system attempts to assign the rider to a provider at a point in time during the departure timeframe when the trip price would be less than or equal to the target trip price. The travel coordination system may also guarantee that the rider will pay no more than the target trip price if the travel coordination system determines that the trip price is likely to be lower than the target trip price at some point in time during the departure timeframe.