Question

Yochanan walked from home to the bus stop at an average speed of

5km/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?

Answer 1

Yochanan covered 30 kilometers by bus and 5 kilometers by walking

Solution:

Let "w" be the distance walking

Let "b" be the distance on the bus

The total distance from his home to school is 35 kilometers

Therefore,

distance walking + distance on the bus = 35

w + b = 35 ----- eqn 1

And the entire trip took 1.5 hours

Time = 1.5 hours

Yochanan walked from home to the bus stop at an average speed of 5km/h

On his school bus and traveled at an average speed of 60 km/h until he got to school

Therefore,

speed on bus = 60 km / hr

speed on walking = 5 km \hr

Time taken is given by formula:

`time = (distance)/(speed)`

Total time = 1.5 hours

time on walk + time on bus = 1.5

`(w)/(5) + (b)/(60) = 1.5`

`(12w+b)/(60) = 1.5\\\\12w+b=90`

12w + b = 90 --------- eqn 2

Subtract eqn 1 from eqn 2

12w + b - w - b = 90 - 35

11w = 55

w = 5

Substitute w = 5 in eqn 1

5 + b = 35

b = 35 - 5

b = 30

Thus he covered 30 kilometers by bus and 5 kilometers by walking