Question:   What is the difference between reaction rate and reaction time?

Answer:

Reaction rate is the rate at which a chemical reaction proceeds.  Rates are usually measured in units of moles per cubic decimeter per second.

Reaction time is the amount of time it takes for a chemical reaction to finish.  If we put two chemicals together, the amount of time it takes for them to fully react is the reaction time.  Because many reactions are equilibria, the reaction time would probably be referred to as the amount of time it takes to achieve equilibrium.

Think of it like taking a car trip to Des Moines, Iowa.  The speed at which your car is traveling to Des Moines is equivalent to the reaction rate, because it tells you how fast you're going.  The amount of time it takes you to get from your house to Des Moines is equivalent to the reaction time, because that's the total amount of time you spent getting to your destination.

When reaction rate increases, reaction time decreases.  Again, imagine driving to Des Moines at ten kilometers an hour.  It'll take a long time to get there.  However, if we increase our speed to 100 kph, the time it takes go get there will go down.

Things that tend to increase reaction rates (and decrease reaction times) include temperature increases and concentration increases.  A good rule of thumb for the dependence of reaction rate on temperature is that for every ten degrees of temperature increase, the rate of a reaction doubles.  The dependence of reaction rate on concentration is somewhat more complicated - depending on the order of the reaction, there may be no effect or a huge effect.  To know for sure, you'll have to take a look at the rate expression.