Her time for the first lap is 50 seconds

Her time for the second lap is 
50 seconds + 20% of 50 seconds =
50 + 0.2×50 = 50 + 10 = 60 seconds.

Her time for the third lap is
60 seconds + 20% of 60 seconds =
60 + 0.2×60 = 60 + 12 = 72 seconds.

Total time = 50 sec + 60 sec + 72 sec =
182 seconds = 3 minutes 2 seconds. 

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Easier and quicker way, but a tiny bit more advanced:

Think of "20% longer" as "120% of", so multiply by 1.2 each time

50+50×1.2+50×1.2×1.2 = 182 seconds = 3 minutes 2 seconds. 

If you have a scientific calculator, you can put in 
50+50×1.2+50×1.2×1.2 in all at one time and press = or "enter".

Edwin