Question

motion of a round trip. a ski lift carried maria up a slope at the rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h. the round trip took 30 min. how far did she ski and for how long?

Explanation:

Step1: Let the time going down (skiing) be $t$ hours.

The total time for the round - trip is 30 minutes or 0.5 hours. So the time going up is $(0.5 - t)$ hours. The distance going up $d_1$ and the distance going down $d_2$ are equal since it's a round - trip. Using the formula $d=rt$ (distance = rate×time), for the upward journey, $d_1 = 6(0.5 - t)$, and for the downward journey, $d_2=34t$.

Step2: Set the two distance equations equal to each other.

Since $d_1 = d_2$, we have $6(0.5 - t)=34t$. Expand the left - hand side: $3-6t = 34t$.

Step3: Solve for $t$.

Add $6t$ to both sides of the equation: $3=34t + 6t$, which simplifies to $3 = 40t$. Then $t=\frac{3}{40}=0.075$ hours.

Step4: Find the distance she skied.

Use the formula $d = rt$ for the skiing (downward) motion. With $r = 34$ km/h and $t = 0.075$ hours, $d=34\times0.075 = 2.55$ km.

Answer:

She skied for $0.075$ hours (or $4.5$ minutes) and skied a distance of $2.55$ km.