Chromatography - How does flow rate affect peak width?

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Main Question or Discussion Point

Today in a lecture on chromatography the lecturer gave an explanation which seems pure ******** to me. The example she used was a handful of solutes, each taking a different path through the stationary phase, obviously some paths will be longer than others and thus each solute will have a different retention time. She said that altering the flow rate doesn't alter the bandwidth (the width of the peak), it just shaves an certain amount of time off the retention time for each solute. For example, it shaves 5 seconds off each analyte (regardless of how long their path is) so that the peak moves down the x axis a bit but doesn't change in width. I'm a visual thinker and my visual image for this concept calls ********. Lets say we have solutes A, B and C and their retention times are:
A = 10s
B = 12s
C = 16s

the way I see it, if I double the flow rate then I will half the retention time for each solute. If I alter the flow rate by a certain amount, then the retention time of each solute will vary depending on their path length. This is a bad example, lets say A, B and C are different compounds with their own specific retention times instead.
If I alter the flow rate by x, my lecturer says that the retention time of each compound will change by y. I say that each compound will change by an amount specific to each compound so the retention time of A will change by ax, B by bx and C by cx, where a, b and c are constants specific to compounds A, B and C. Can anyone here shed light on this? Who is right, me or my lecturer? I kept my mouth shut during the lecture cuz I couldn't think of the words to convey what I see.
 

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