Before going to school, Eudora ran from her home to her secret laboratory at an average speed of 12 km/h. She then took one of her jetpacks and flew to her school at an average speed of 76 km/h. Eudora traveled a total distance of 120km, and the entire trip took 2 hours. How long did Eudora spend running, and how long did she spend flying using her jetpack?

she flew 1h 30m and ran 30m

Step-by-step explanation:

First we have to make 2 equations, one that represents the distance that it traveled and another that represents the time that it ran

x = time she ran

y = time she flew

x + y = 2h

x * 12 + y * 76 = 120

we clear x in the first equation

x + y = 2

x = 2 - y

we replace x with (2 - y) in the second equation

x * 12 + y * 76 = 120

(2 - y) * 12 + y * 76 = 120

24 - 12y + 76y = 120

-12y + 76y = 120 - 24

64y = 96

y = 96/64

y = 3/2

this means that 1 hour and a half was flying

x = 2 - y

x = 2 - 3/2

x = 1/2

this means that half hour was runing