Question

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?

Answer 1

Answer:

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.