Respuesta :
Answer:
Eudora spent 0.5 hours in running and 1.5 hours flying using her jet-pack.
Step-by-step explanation:
Let x represent time spent in running.
We have been given that the entire trip took 2 hours, so time spent in flying the jet-packs would be [tex]2-x[/tex].
We know that distance is equal to speed times time.
[tex]\text{Distance}=\text{Speed}\times\text{Time}[/tex]
Eudora ran from her home to a secret laboratory at an average speed of 12 km, so distance traveled by running would be [tex]12x[/tex].
Eudora took one of her jet-packs and flew to her school at an average speed of 76 km, so distance covered by jet-packs would be [tex]76(2-x)[/tex].
We are told that Eudora traveled a total distance of 120 km. We can represent this information in an equation as:
[tex]12x+76(2-x)=120[/tex]
[tex]12x+152-76x=120[/tex]
Combine like terms:
[tex]-64x+152=120[/tex]
[tex]-64x+152-152=120-152[/tex]
[tex]-64x=-32[/tex]
Divide both sides by [tex]-64[/tex]:
[tex]\frac{-64x}{-64}=\frac{-32}{-64}[/tex]
[tex]x=0.5[/tex]
Therefore, Eudora spent 0.5 hours in running.
Upon substituting [tex]x=0.5[/tex] in expression for time spent in flying jet-packs, we will get:
[tex]2-x\Rightarrow 2-0.5=1.5[/tex]
Therefore, Eudora spent 1.5 hours flying using her jet-pack.
