"Long time" is a phrase which is often translated as "mucho tiempo", and "a long time" is a phrase which is also often translated as "mucho tiempo". Learn more about the difference between "long time" and "a long time" below.
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A phrase is a group of words commonly used together (e.g once upon a time).
a. mucho tiempo
I had to wait a long time to see the doctor.Tuve que esperar mucho tiempo para ver al médico
He took a long time to finish eating his food.Tardó mucho en terminar comiendo su cena.