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 (square) kilometers and traveled (square) kilometers on the bus.

Explanation:

Step1: Define variables for distances

Let $x$ = walking distance (km), $y$ = bus distance (km).

Step2: Set total distance equation

Total distance is 35 km:
$$x + y = 35$$

Step3: Set total time equation

Time = distance/speed. Total time is 1.5 h:
$$\frac{x}{5} + \frac{y}{60} = 1.5$$

Step4: Simplify time equation

Multiply all terms by 60 to eliminate denominators:
$$12x + y = 90$$

Step5: Solve the system of equations

Subtract the total distance equation from the simplified time equation:
$$(12x + y) - (x + y) = 90 - 35$$
$$11x = 55$$
$$x = 5$$

Step6: Find bus distance

Substitute $x=5$ into $x + y = 35$:
$$5 + y = 35$$
$$y = 30$$

Answer:

Yochanan walked 5 kilometers and traveled 30 kilometers on the bus.