Question

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

Answer 1

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 $2-x$.

We know that distance is equal to speed times time.

$\text{Distance}=\text{Speed}\times\text{Time}$

Eudora ran from her home to a secret laboratory at an average speed of 12 km, so distance traveled by running would be $12x$.

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 $76(2-x)$.

We are told that Eudora traveled a total distance of 120 km. We can represent this information in an equation as:

$12x+76(2-x)=120$

$12x+152-76x=120$

Combine like terms:

$-64x+152=120$

$-64x+152-152=120-152$

$-64x=-32$

Divide both sides by $-64$:

$\frac{-64x}{-64}=\frac{-32}{-64}$

$x=0.5$

Therefore, Eudora spent 0.5 hours in running.

Upon substituting $x=0.5$ in expression for time spent in flying jet-packs, we will get:

$2-x\Rightarrow 2-0.5=1.5$

Therefore, Eudora spent 1.5 hours flying using her jet-pack.