Question

Yochanan walked from home to the bus stop at an average speed of 5 \text{km/h}km/hstart text, k, m, slash, h, end text. He immediately got on his school bus and traveled at an average speed of 60 \text{km/h}km/hstart text, k, m, slash, h, end text until he got to school. The total distance from his home to school is 35 kilometers, and the entire trip took 1.5, point, 5 hours.How many kilometers did Yochanan cover by walking, and how many kilometers did he cover by travelling on the bus?

Answer 1

Answer:the distance that Yochanan covered by walking is 5km/h

the distance that Yochanan covered by travelling on the bus is 30km/h

Explanation:

Let x represent the distance that Yochanan covered by walking.

Let y represent the distance that Yochanan covered by travelling on the bus.

The total distance from his home to school is 35 kilometers. This means that

x + y = 35

Distance travelled = speed × time.

time = Distance/speed

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

Time it took him to walk to the bus top would be

t = x/5 hours

He immediately got on his school bus and traveled at an average speed of 60 km/h.

Time taken to travel on the bus would be

t = y/60 hours

Since the total time spent on the trip is 1.5hours, then

x/5 + y/60 = 1.5

12x + y = 90 - - - - - - - - --1

Substituting x = 35 - y into equation 1, it becomes

12(35 - y) + y = 90

420 - 12y + y = 90

- 12y + y = 90 - 420

- 11y = - 330

y = -330/-11 = 30

Substituting y = 30 into x = 35 - y, it becomes

x = 35 - 30 = 5

Answer 2

Yochanan covered 5 kilometers by walking.

Yochanan covered 30 kilometers by travelling on the bus.

Explanation:

Let w represent distance walked.

We have been given that the total distance from his home to school is 35 kilometers. So distance covered by the bus would be
`35-w`.

`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`

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

`\frac{\text{Distance walked}}{\text{ Walking speed}}=(w)/(5)`

He immediately got on his school bus and traveled at an average speed of 60 km/h until he got to school. So,

`\frac{\text{Distance covered by bus}}{\text{ Bus's speed}}=(35-w)/(60)`

We are told that the entire trip took 1.5 hours. We can represent our information as:

`(w)/(5)+(35-w)/(60)=1.5`

Let us solve for w.

`(w)/(5)*60+(35-w)/(60)*60=1.5*60`

`12w+35-w=90`

`11w+35-35=90-35`

`11w=55`

`(11w)/(11)=(55)/(11)`

`w=5`

Therefore, Yochanan covered 5 kilometers by walking.

Now, we will substitute
`w=5` in expression
`35-w` to find distance covered by travelling on the bus as:

`35-w\Rightarrow 35-5=30`

Therefore, Yochanan covered 30 kilometers by travelling on the bus.