Eudora ran from her home to her secret laboratory at an average speed of 12/text{ km/h}12 km/h12, start text, space, k, m, slash, h, end text. She then took one of her jetpacks and flew to her school at an average speed of 76/text{ km/h}76 km/h76, start text, space, k, m, slash, h, end text. 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 30 minutes and use the jetpack for 1 hour and 30 minutes

Step-by-step explanation:

Lets call x the time she ran and y the time she was using a jetpack (in hours), we have

12x + 76y = 120

Since it took 2 hours we have that x+y = 2, hence y = 2-x. We can replace y in the equation above, obtaining

12x + 76 (2-x) = 120

12x + 152 - 76x = 120

12x-76x = 120-152

-64x = - 32

x = - 32/-64 = 1/2 (30 minutes)

As a result

y = 1-1/2 = 3/2 (1 hour, 30 minutes)

She ran for 30 minutes and use the jetpack for 1 hour and 30 minutes.