Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, space, k, m, slash, h. she then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, space, k, m, slash, h. eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours. how long did eudora spend running, and how long did she spend flying using her jetpack? eudora ran for hours and flew for hours using her jetpack.

Let x be the amount of time she runs.  12x would then represent the distance she runs (d=rt; distance = speed (rate) * time).  2-x, or the total time minus the time she spends running, would be the amount of time she uses her jetpack.  76(2-x) would then represent the distance she flies on her jetpack.  We know the total distance is 120 km; so 
12x + 76(2-x) = 120
Use the Distributive Property:
12x + 76*2 - 76*x = 120
12x + 152 - 76x = 120
Combine like terms:
-64x + 152 = 120
Cancel the 152 by subtracting:
-64x + 152 - 152 = 120 - 152
-64x = -32
Cancel the -64 by dividing:
-64x/-64 = -32/-64
x = 0.5
She runs for 0.5 hours.  She would use her jetpack for 2-0.5=1.5 hours.