Assuming there is nothing connected to the Vout terminals, then yes, the current is the same in both resistors. Also, BTW, electrons do not "slow down".
Intuitively, think of it this way. The mobile electrons have to go somewhere. At two different points on a highway with no exits in-between, all of the cars going past point A have to go past point B. In a simple series circuit with ((any)) number of components of any type (resistors, capacitors, inductors, diodes, whatever), 100% of the current goes through 100% of the components 100% of the time. The nature of the components has a direct effect on what that current is, but all of the energy is "trapped' in the loop.
For a string of resistors, the current is determined by the total resistance of the string. Inside the string, the voltage across each individual resistor is directly proportional to its resistance, per Ohm's Law. As an exercise, draw up a string of four resistors in series with the values of 1, 2, 3, and 4 ohms, connected to a 10 V battery. First, calculate the current through the string, then use that current to calculate the voltages across each resistor, then add up those individual voltages and compare that number to the battery voltage.
A similar thing is true with parallel circuits. With 2 or more resistors in parallel, 100% of the voltage appears across 100% of the components 100% of the time. This time, again using Ohm's Law, the current through each resistor is inversely proportional to the value of the resistor.