Question

yochanan walked from home to the bus stop at an average speed of 5 km/h. he immediately got on his school bus and traveled at an average speed of 60 km/h until he got to school. the total distance from his home to school is 35 kilometers, and the entire trip took 1.5 hours. how many kilometers did yochanan cover by walking, and how many kilometers did he cover by travelling on the bus? yochanan walked kilometers and traveled kilometers on the bus.

Explanation:

Step1: Define Variables

Let \( x \) be the distance walked (in km), so the distance traveled by bus is \( 35 - x \) km.

Step2: Time Formula

Time = Distance / Speed. Time walking: \( \frac{x}{5} \), time by bus: \( \frac{35 - x}{60} \). Total time is 1.5 hours, so:

$$ \frac{x}{5} + \frac{35 - x}{60} = 1.5 $$

Step3: Solve Equation

Multiply all terms by 60 (LCM of 5, 60) to eliminate denominators:

$$ 12x + 35 - x = 90 $$

Simplify: \( 11x + 35 = 90 \) → \( 11x = 55 \) → \( x = 5 \).

Step4: Find Bus Distance

Bus distance: \( 35 - 5 = 30 \) km.

Answer:

Yochanan walked \( \boldsymbol{5} \) kilometers and traveled \( \boldsymbol{30} \) kilometers on the bus.